Printable math worksheet for calculating the area of composite figures using given dimensions.

Let’s solve each composite figure one by one. We’ll break them into simpler shapes (like rectangles, triangles, semicircles) and add or subtract areas as needed.

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Figure 1 (Top Left):
It’s an L-shape. Break it into two rectangles:
- Top rectangle: 8 × 3 = 24
- Bottom right rectangle: 5 × (6 - 3) = 5 × 3 = 15
Wait — actually, better to think: total height is 6, left part has a cutout of 4 down from top? Let me recheck.

Actually, looking at the drawing:
Total width = 8, total height = 6.
There’s a notch on the bottom left: width 3, height 4? Wait no — labels are:

Top horizontal: 8
Right vertical: 6
Bottom horizontal: 5
Left side has a step: 3 across, then 4 down.

So we can split vertically:
Left part: width 3, height 4 → area = 3×4=12
Right part: width 5, height 6 → area = 5×6=30
But wait — that overlaps? No.

Better way: Think of full rectangle minus missing piece.

Full rectangle if no cut: 8 × 6 = 48
Missing piece: bottom left corner, which is 3 wide and 4 high? But the bottom is labeled 5, so the missing part is (8-5)=3 wide, and height is 4? Yes.

So missing area = 3 × 4 = 12
Area = 48 - 12 = 36

✔ Check: Alternatively, top rectangle 8×(6-4)=8×2=16, plus bottom rectangle 5×4=20 → 16+20=36. Same.

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Figure 2:
L-shape again.
Top: 7 wide, right side 6 tall.
Bottom right: 2 wide, and there's a step up of 3.

Split into:
Top rectangle: 7 × (6 - 3) = 7 × 3 = 21
Bottom right rectangle: 2 × 3 = 6
Total = 21 + 6 = 27

Or: Full rectangle 7×6=42, minus missing left-bottom part: width (7-2)=5, height 3 → 5×3=15 → 42-15=27. Same.

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Figure 3:
Looks like a big rectangle with a small rectangle on top.

Big rectangle: base 12, height 5 → 12×5=60
Small rectangle on top: width? The top has 6 and 4 on sides, so middle part is 12 - 6 - 4 = 2? And height 3 → area = 2×3=6
Total = 60 + 6 = 66

Wait — check: the 6 and 4 are on the sides of the top bump? Actually, the diagram shows:

Top: left segment 6, then a bump up of height 3, then right segment 4. So the bump width is 12 - 6 - 4 = 2. Yes.

So yes, 60 + 6 = 66

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Figure 4:
Rectangle with semicircle on top.

Rectangle: width 4, height 8 → 4×8=32
Semicircle: diameter = 4 → radius = 2 → area = (πr²)/2 = (π×4)/2 = 2π ≈ 6.28
But since answers are in square units and likely expect exact or simplified, but problem says “answers are in square units” — probably want numerical value? But in school worksheets, sometimes they leave π, but here numbers are integers — maybe approximate?

Wait — look at other figures — all have integer answers. Probably this one expects us to use π≈3.14? But let’s see.

Actually, in many such problems, if it’s a semicircle, they might expect you to compute numerically.

But let’s hold — perhaps I should assume π=3.14 for now.

Area = 32 + (1/2)×π×(2)^2 = 32 + 2π ≈ 32 + 6.28 = 38.28 — not integer.

Wait — maybe I misread. Is the semicircle on top of the rectangle? Yes. Diameter equals width of rectangle = 4.

But perhaps the worksheet expects exact form? Unlikely — others are integers.

Alternative: Maybe the dotted line is the diameter, and we’re to include only the shape — but still.

Wait — let me check Figure 10 later — same thing.

Perhaps for now, I’ll calculate with π=3.14 and round? But let’s see the pattern.

Actually, looking ahead — Figure 10 also has semicircle. Maybe both are meant to be calculated with π.

But the instruction says “Answers are in square units” — doesn’t specify decimal or fraction.

To be safe, I’ll compute exactly and see.

But for consistency, let’s do all with π=3.14 unless specified.

So Figure 4: 32 + 2*3.14 = 32 + 6.28 = 38.28 — but that seems messy.

Wait — perhaps I made a mistake. Is the semicircle added or is it part of the figure? Yes.

Another thought: maybe the 8 includes the semicircle? No, the 8 is the straight side.

Looking back at the image description: "8" is the height of the rectangle, "4" is the width, and semicircle on top.

I think we have to go with 32 + 2π. But since other answers are integers, perhaps this is an exception.

Wait — let’s skip and come back. Maybe I’ll calculate all and see.

For now, I’ll note it as 32 + 2π, but for final answer, perhaps they want numerical.

Actually, let me check online or standard practice — in many elementary worksheets, they use π=3.14 and expect decimal.

But to match format, perhaps I should use π=3.14.

Let me proceed with that assumption.

So Figure 4: 32 + 2*3.14 = 32 + 6.28 = 38.28 — but let's keep more precision or see.

Actually, 2π is approximately 6.2832, so 38.2832 — but probably round to two decimals? Or maybe they expect 38.3? But others are integers.

This is confusing. Let me look at Figure 10 — same issue.

Perhaps for these, the answer is expected as 32 + 2π, but since the problem says "answers are in square units", and no specification, I'll compute numerically with π=3.14.

So 38.28 — but let's write as 38.3? No, better to use exact calculation.

Another idea: perhaps the semicircle area is to be calculated as (πd²)/8 or something — no.

I recall that in some curricula, they use π=22/7.

Let me try that: π=22/7, so 2π = 44/7 ≈ 6.2857, still not integer.

Perhaps the figure is different. Let me double-check the dimensions.

In Figure 4: rectangle 4x8, semicircle on top with diameter 4.

Yes.

Maybe the 8 is the total height including semicircle? But the label "8" is next to the straight side, so likely the rectangle height.

I think I have to accept it's not integer. But let's move on and come back.

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To save time, I'll solve all figures systematically.

Let me list all 20 figures and solve one by one.

Figure 1:
As above, 36

Figure 2:
27

Figure 3:
66

Figure 4:
Rectangle: 4 * 8 = 32
Semicircle: radius 2, area = (1/2)*π*4 = 2π ≈ 6.2832
Total ≈ 38.2832 — but perhaps they want 38.3 or 38.28? I'll use 38.28 for now, but let's see later.

Actually, upon second thought, in many such worksheets, for semicircles, they might expect the answer as a number using π=3.14, so 38.28, but rounded to nearest whole number? 38.

But 2*3.14=6.28, 32+6.28=38.28, so perhaps 38.3, but I think for accuracy, I'll keep it as 38.28, but let's check Figure 10.

Figure 10: similar, rectangle 22x10? Wait no.

Figure 10: it's a rectangle with semicircle on left end.

Dimensions: the straight part is 22 long, height 10, and semicircle on left with diameter 10.

So area = rectangle 22*10 = 220, plus semicircle (1/2)*π*(5)^2 = (1/2)*π*25 = 12.5π ≈ 39.25, total 259.25

Again not integer.

Perhaps the worksheet allows decimals, or perhaps I need to use π=3.14 consistently.

I'll proceed with π=3.14 for all semicircle calculations.

So for Figure 4: 32 + 2*3.14 = 32 + 6.28 = 38.28

But to match the format, perhaps they expect two decimals or something. I'll write it as 38.28 for now.

Let's continue.

Figure 5:
U-shape or something.

Top: 10 wide, right side 8 tall.
Bottom has two legs of 2 each, and a gap of ? The bottom is not given, but from the drawing, the total width is 10, and there are two segments of 2 at bottom, so the middle gap is 10 - 2 - 2 = 6, and the depth of the U is 2 (since it says "2" inside).

So area = full rectangle minus the missing rectangle in the middle.

Full rectangle: 10 * 8 = 80
Missing rectangle: width 6, height 2 → 12
Area = 80 - 12 = 68

Alternatively, three parts: left leg 2*8=16, right leg 2*8=16, bottom middle 6*2=12? No, that's not right because the bottom is only 2 high, but the legs are full height.

Better: the shape is like a frame.

The outer rectangle is 10x8=80.
The inner cutout is a rectangle of width (10-2-2)=6 and height 2, so 12.
So 80-12=68. Yes.

Figure 6:
Trapezoid or something.

Left side 12, bottom 14, right side 4, and a slant.

From the drawing, it's a trapezoid with parallel sides 12 and 4, and height? The bottom is 14, but the top is not given.

Actually, it looks like a rectangle with a triangle on top or something.

Let's see: the right side is 4, bottom is 14, left side is 12, and there's a diagonal from top-left to a point on the bottom.

The horizontal distance from left to the start of the flat top is not given, but there's a label "6" on the top right part.

The top has a horizontal segment of 6, and the total bottom is 14, so the overhang on left is 14 - 6 = 8? But the left side is 12, right side is 4, so the difference in height is 8, and the horizontal run is 8, so it's a right triangle on the left.

Yes! So the figure can be seen as a rectangle on the right: width 6, height 4 → area 24
Plus a triangle on the left: base 8 (since 14-6=8), height 8 (12-4=8) → area (1/2)*8*8=32
Total = 24 + 32 = 56

Confirm: the triangle has legs 8 and 8, yes.

Figure 7:
L-shape.

Total height 20, total width? Not given directly.

Labels: left side 10, bottom? , top right 7, and a horizontal 12.

From the drawing, it's like a large rectangle with a bite taken out, but let's split.

We can split into two rectangles:
- Bottom rectangle: width say W, height 10
- Top right rectangle: width 7, height (20-10)=10

But what is the width of the bottom? The horizontal label "12" is on the top of the bottom part, so probably the bottom rectangle has width 12, height 10 → area 120
Top right rectangle: width 7, height 10 → area 70
But do they overlap? No, because the top right is attached to the right of the bottom.

Total width would be 12 + 7 = 19, but is that correct? The left side is 10, which matches the bottom height.

Yes, so area = 12*10 + 7*10 = 120 + 70 = 190

Is that right? The total height is 20, and we have two parts each of height 10, stacked? No, they are side by side in a way.

Actually, the bottom rectangle is 12 wide and 10 high, sitting at the bottom.
Then on top of the right part of it, there is a rectangle 7 wide and 10 high, so total height on the right is 20, on the left is 10.

Yes, so no overlap, area 120 + 70 = 190.

Figure 8:
Z-shape or something.

Labels: top 6, right side 3, then down 6, then left 3, then down 3, then left 6.

So it's like two rectangles connected.

We can split into:
- Top rectangle: 6 x 3 = 18
- Middle rectangle: but it's offset.

Notice that the total height is 3 + 6 + 3 = 12? Let's see the vertical segments.

From top to bottom: first down 3, then down 6, then down 3, so total height 12.
Width: at top 6, then after going down 3, it goes left 3, so the middle part is narrower.

Actually, it's composed of three rectangles:
- Top: 6 wide, 3 high → 18
- Middle: width (6-3)=3? When it goes left 3, so the middle section is 3 wide, and height 6 → 3*6=18
- Bottom: 6 wide, 3 high → 18
But are they aligned? The bottom is shifted left by 3, so yes, no overlap.

Total area = 18 + 18 + 18 = 54

Confirm: the shape is symmetric in a way.

Figure 9:
Irregular polygon.

Labels: bottom 18, right side 10, top has 8 and 4, and a slant.

From the drawing, it's a trapezoid with a rectangle on top or something.

Let's see: the bottom is 18, right side is 10, then on top, there is a horizontal segment of 8, and to the left of it, a vertical drop of 4, then a slant to the bottom left.

So, we can split into:
- Rectangle on right: width 8, height 10 → 80
- Triangle on left: base? The total bottom is 18, rectangle takes 8, so remaining base is 10, but the height of the triangle is the difference in height.

The left side has a vertical drop of 4 from the top, so the triangle has height 4, and base 18 - 8 = 10? But is it a right triangle?

From the top-left of the rectangle, it goes down 4, then slants to the bottom-left corner.

So the horizontal distance from the drop point to the left end is 18 - 8 = 10, and vertical drop is 4, so yes, a right triangle with legs 10 and 4.

Area of triangle = (1/2)*10*4 = 20
Rectangle = 8*10 = 80
Total = 80 + 20 = 100

But is the rectangle height 10? The right side is labeled 10, and the rectangle is on the right, so yes.

Figure 10:
Arrow shape.

Bottom rectangle: width 6, height 4 → 24
Top triangle: base? The total width at the top of the rectangle is 6, but the arrowhead extends.

Labels: on the sides, "2" and "4", and height of triangle is 10.

From the drawing, the triangle has height 10, and the base of the triangle is the width at the top of the rectangle plus the extensions.

The rectangle is 6 wide, and on each side, there is a "2" label, which might be the overhang.

Typically in such arrows, the triangle base is wider than the rectangle.

Here, the labels "2" are on the sides of the rectangle, and "4" below, but let's see.

The dotted line is the height of the triangle, 10.

The base of the triangle: from the drawing, the total width at the base of the triangle is 6 + 2 + 2 = 10? Because the rectangle is 6, and on each side, there is a 2-unit extension for the triangle.

Yes, so base of triangle = 6 + 2 + 2 = 10
Height = 10
Area of triangle = (1/2)*10*10 = 50
Rectangle = 6*4 = 24
Total = 50 + 24 = 74

The "4" is the height of the rectangle, yes.

Figure 11:
L-shape with a bite.

Labels: left 22, bottom 24, top 16, right has 15 and 8.

So, it's like a large rectangle with a smaller rectangle cut out from the top right.

Full rectangle: 24 * 22 = 528
Cut-out rectangle: width? The top is 16, so the cut-out width is 24 - 16 = 8? And height is 15? But the right side has 15 and 8, so probably the cut-out is 8 wide and 15 high.

Yes, because from the top, it goes down 15, then right 8, but wait.

Actually, the shape has a notch on the top right.

The total width is 24, the top horizontal is 16, so the notch width is 24 - 16 = 8.
The height of the notch is 15, as labeled.

So area = full rectangle minus notch = 24*22 - 8*15 = 528 - 120 = 408

Confirm: 24*22=528, 8*15=120, yes.

Figure 12:
L-shape.

Labels: top 12, right side 3, then down, then left 5, then down, then left 16? Wait.

From the drawing: top horizontal 12, then down 3, then left 5, then down, then left to make total left side 16.

So, we can split into two rectangles:
- Top rectangle: 12 x 3 = 36
- Bottom rectangle: width? The total left side is 16, and the top part is 3 high, so bottom part height is 16 - 3 = 13? But the bottom width is not given.

When it goes left 5 after down 3, so the bottom rectangle has width 12 - 5 = 7? Let's see.

After going down 3 from top-right, it goes left 5, so the bottom part starts at x=5 from left? Total width is 12, so if it goes left 5 from the right, that means from left, it's at 12-5=7.

Then it goes down to total height 16, so the bottom rectangle is from y=3 to y=16, height 13, and width 7 (from x=0 to x=7?).

The left side is labeled 16, which is the total height.

So bottom rectangle: width 7, height 13 → 91
Top rectangle: 12 x 3 = 36
But do they overlap? The top rectangle is from y=0 to y=3, x=0 to x=12.
Bottom rectangle is from y=3 to y=16, x=0 to x=7.
So no overlap, total area = 36 + 91 = 127

Is the width of bottom really 7? When it goes left 5 from the right end, and total width is 12, so yes, the bottom part extends from left to x=7.

Yes.

Figure 13:
Large L-shape.

Labels: left 30, bottom 34, top 8, and a horizontal 15.

So, similar to before.

Full rectangle if no cut: 34 * 30 = 1020
Cut-out rectangle: width? The top is 8, so the cut-out width is 34 - 8 = 26? Height is 15? But the label "15" is on the vertical part.

From the drawing, after the top 8, it goes down 15, then right to make the bottom 34.

So the cut-out is a rectangle of width (34 - 8) = 26, height 15.

Area = 34*30 - 26*15 = 1020 - 390 = 630

Calculate: 26*15=390, yes, 1020-390=630.

Figure 14:
Rectangle with semicircle on left.

Rectangle: length 22, height 10 → 220
Semicircle: diameter 10, radius 5 → area = (1/2)*π*25 = 12.5π ≈ 12.5*3.14 = 39.25
Total = 220 + 39.25 = 259.25

Figure 15:
Square with a bite.

Labels: top 16, right side has 5 and 15, bottom 20.

So, full rectangle 20 * ? Height is not given directly.

Left side is not labeled, but from the drawing, the total height is 5 + 15 = 20? Because on the right, it goes down 5, then down 15, so total height 20.

Width is 20 at bottom, 16 at top, so it's like a rectangle with a notch on the top right.

Full rectangle: 20 * 20 = 400
Notch: width 20 - 16 = 4, height 5 → area 20
Area = 400 - 20 = 380

Confirm: the notch is 4 wide and 5 high, yes.

Figure 16:
L-shape.

Labels: top 9, right side 12, then down, then right 7, then down, then left 18.

So, total width 18, total height? Left side not given, but from top to bottom: first down 12, then down to make total height.

After going down 12 from top-right, it goes right 7, then down, then left 18.

So, the bottom part has width 18, and the top part has width 9.

The height of the top part is 12, and the bottom part height is not given, but the total height can be found.

When it goes right 7 after down 12, so the bottom rectangle starts at x=9 from left? Total width 18, top is 9, so the bottom extends full width.

Actually, the shape is: top rectangle 9 wide, height 12.
Then below it, a rectangle that is 18 wide, but how high? The label "7" is on the horizontal after the down 12, but that might be the width of the connection.

Let's think: from the top-left, go right 9, down 12, then right 7, then down H, then left 18, then up to start.

The total width is 18, and after going right 9 + 7 = 16, then left 18, so the bottom must extend left by 2 more, but that doesn't make sense.

Perhaps the "7" is the height of the bottom part? No, it's labeled on a horizontal segment.

Looking at the drawing: it's an L-shape rotated.

Standard way: the vertical part on left is 12 + something, but let's calculate the area by splitting.

Split into:
- Left rectangle: width 9, height 12 + H, but H unknown.

Notice that the total width is 18, and the top part is 9 wide, so the bottom part must be 18 wide, and the height of the bottom part is the distance from the bottom of the top rectangle to the bottom.

The label "7" is on the horizontal segment that connects, but in the drawing, after going down 12, it goes right 7, which means that the bottom rectangle is offset.

Actually, the bottom rectangle has width 18, and it starts at x=0 to x=18, but the top rectangle is from x=0 to x=9, y=0 to y=12.

Then from (9,12) it goes right to (16,12), then down to (16,12+H), then left to (0,12+H), then up to (0,0)? But that would require the left side to be 12+H, and the bottom is 18, but the path from (16,12+H) to (0,12+H) is 16 units, not 18.

I think I have it wrong.

From the labels: top horizontal 9, then down 12, then right 7, then down, then left 18, then up.

So, the last left 18 suggests that the bottom width is 18, and it goes from right to left 18 units.

So, let's trace the perimeter.

Start at top-left: go right 9, down 12, right 7, down D, left 18, up U.

For it to close, the net displacement must be zero.

Horizontally: +9 +7 -18 = -2, so not closed. That can't be.

Perhaps the "left 18" is from the current position, but after going down D, it is at x=9+7=16, y=12+D, then left 18 to x=16-18= -2, which is impossible.

I think there's a mistake in my interpretation.

Looking back at the user's image description, for Figure 16: "9" on top, "12" on the right vertical, "7" on the bottom right horizontal, "18" on the bottom.

Probably, the shape is: a rectangle on top 9x12, and a rectangle on bottom that is 18 wide, but the bottom rectangle is attached to the right part.

So, the bottom rectangle has width 18, height H, and it is positioned such that its left end is at x=0, but the top rectangle is from x=0 to x=9, so the bottom rectangle extends from x=0 to x=18, so it overlaps with the top rectangle from x=0 to x=9.

Then the area would be top rectangle 9*12 = 108, plus bottom rectangle 18*H, but minus the overlap 9*H, so net 108 + 9*H.

But what is H? The label "7" is on the horizontal after the down 12, which might be the width of the protrusion, but in this case, after going down 12 from (9,0) to (9,12), then right 7 to (16,12), then down to (16,12+H), then left to (0,12+H), then up to (0,0).

Then the bottom width is from x=0 to x=16, but the label says "18" on the bottom, so contradiction.

Perhaps the "18" is the total width, and "7" is the height of the bottom part.

Let's assume that the bottom part has height 7.

Then, the shape is: top rectangle 9x12 = 108
Bottom rectangle: width 18, height 7 = 126
But they overlap in the region where both exist, which is 9x7 = 63
So total area = 108 + 126 - 63 = 171

Is that correct? In composite figures, if they share a common region, we subtract once.

But in this case, the bottom rectangle is below the top, so if the top is from y=0 to y=12, bottom from y=12 to y=19, then no overlap.

The label "7" might be the height of the bottom part.

In the drawing, after going down 12, it goes right 7, which might mean that the bottom part is only under the right part.

Let's try this: the top rectangle is 9 wide, 12 high.
Then, attached to its right side, a rectangle that is 7 wide and H high, but then the bottom is 18, so perhaps the bottom rectangle is 18 wide and K high, but it's complicated.

Another way: the total area can be calculated as the area of the bounding box minus cutouts, but let's look for a better approach.

From the labels, the total width is 18, total height is 12 + 7 = 19? Because the "7" might be the additional height.

Assume that the bottom part has height 7, and width 18, and the top part is 9x12, but the top part is sitting on the left part of the bottom rectangle.

So, the bottom rectangle is 18x7 = 126
The top rectangle is 9x12 = 108, but it is placed on top of the left 9 units of the bottom rectangle, so the combined shape has the bottom rectangle, and on top of its left half, the top rectangle.

So no overlap in area, since they are at different y-levels.

If the bottom rectangle is from y=0 to y=7, x=0 to x=18.
Top rectangle from y=7 to y=19, x=0 to x=9.
Then area = 18*7 + 9*12 = 126 + 108 = 234

And the label "7" is the height of the bottom part, "12" is the height of the top part, "9" is width of top, "18" is width of bottom.

Yes, that makes sense.

So area = 18*7 + 9*12 = 126 + 108 = 234

Figure 17:
T-shape.

Labels: top 32, right side 14, bottom has 11,9,16.

So, the top bar is 32 wide, 14 high? But the right side is 14, which might be the height of the top bar.

Then the stem is below, with width 9, and the bottom has segments 11,9,16, sum 36, but top is 32, so not matching.

Probably, the top bar is 32 wide, height H, and the stem is 9 wide, height K.

From the drawing, the right side label "14" is likely the height of the top bar.

Then the stem is centered or something.

The bottom has three segments: 11,9,16, sum 36, but the top is 32, so perhaps the stem is 9 wide, and the top bar extends beyond.

The total width at bottom is 11+9+16=36, at top is 32, so the top bar is narrower.

Perhaps the top bar is 32 wide, and the stem is 9 wide, and the stem is attached to the bottom of the top bar.

Then the area = area of top bar + area of stem.

Top bar: 32 * 14 = 448
Stem: 9 * H, but H is not given.

The bottom has labels 11,9,16, which might be the widths of the parts, but for the stem, it's 9 wide, and the height is not given.

Perhaps the "14" is the total height, but that doesn't make sense.

Another interpretation: the shape is like a T, with the top bar 32 wide, and the stem 9 wide, and the height of the stem is such that the total height is given, but not.

Look at the bottom: the segments 11,9,16 suggest that the bottom width is 36, and the stem is 9 wide, so the top bar must be wider or narrower.

Perhaps the top bar is 32 wide, and it is centered, so on each side, there is an overhang.

The bottom width is 11+9+16=36, so the top bar is 32, so overhang on left and right.

But for area, we need heights.

The label "14" is on the right side, which is likely the height of the top bar.

Then the stem has height, say, S, but not given.

Perhaps the "14" is the total height, but then the stem height would be 14 minus something.

I think I need to assume that the top bar has height 14, and the stem has height H, but H is not given.

Unless the bottom labels indicate the height, but they are on the bottom, so probably widths.

Perhaps the 11,9,16 are not widths, but something else, but in the context, likely widths of the bottom segments.

Another idea: the shape is composed of three rectangles: left arm, stem, right arm, but it's a T, so probably not.

Let's calculate the area as the top rectangle minus the cutouts, but it's additive.

Perhaps the stem is 9 wide, and the top bar is 32 wide, and the height of the top bar is 14, and the height of the stem is the distance from the bottom to the top bar, but not given.

I recall that in some T-shapes, the stem height is given by the difference, but here not.

Look at the numbers: bottom has 11,9,16, sum 36, top is 32, so perhaps the top bar is inset.

Perhaps the "14" is the height of the entire figure, but then the stem height would be less.

Assume that the top bar has height H_t, stem has height H_s, but only one number 14.

Perhaps 14 is the height of the stem, and the top bar height is not given, but that doesn't help.

Let's read the label: "14" is on the right side, and for a T-shape, it might be the height of the top bar.

Then for the stem, the height can be inferred from the bottom, but no.

Another thought: the bottom segments 11,9,16 might be the lengths, but for the area, we can consider the shape as a large rectangle minus two rectangles on the sides.

For example, the bounding box is 36 wide (11+9+16) and height 14 + H_s, but H_s unknown.

Perhaps the 14 is the total height, and the top bar is at the top, so the stem height is 14 - H_t, but H_t unknown.

I think there's a standard way.

Let's look at the values: perhaps the top bar is 32 wide, and the stem is 9 wide, and the height of the top bar is 14, and the height of the stem is the same as the "9" or something, but that doesn't make sense.

Perhaps the "9" in the bottom is the width of the stem, and the "11" and "16" are the overhangs, but for the top, it's 32, so the overhang on left is (32 - 9)/2 or something, but 32-9=23, not divisible.

32 - 9 = 23, and 11+16=27, not match.

Perhaps the top bar is not full width; let's calculate the area as sum of parts.

Suppose the top bar is 32 wide, height A.
The stem is 9 wide, height B.
Then area = 32A + 9B.

From the drawing, the right side label "14" might be A, so A=14.
Then B is not given, but perhaps from the bottom, the total height is A + B, but not given.

Unless the "14" is the total height, then B = 14 - A, but A unknown.

I think I found a better way: in the bottom, the segments 11,9,16 are the widths of the three parts at the bottom, but for the T-shape, the bottom is only the stem, so why three segments?

Perhaps it's not a T, but a different shape.

Looking back at the user's description: "32" on top, "14" on right, "11" "9" "16" on bottom.

Probably, the shape is like a rectangle with a protrusion at the bottom center.

So, the main body is 32 wide, height H, and at the bottom, a stem of width 9, height K.

Then the bottom has the stem width 9, and on left and right, the main body extends, so the bottom width is 32, but the labels show 11,9,16, sum 36, which is larger than 32, so not.

Unless the main body is narrower.

Perhaps the top is 32, but the bottom is wider, so it's like a trapezoid, but with a stem.

I think I need to assume that the "11", "9", "16" are the widths of the bottom, and the "14" is the height of the top part, and the stem height is given by the context.

Perhaps the height of the stem is 9, but that's used for width.

Let's calculate the area as the area of the top rectangle plus the area of the stem rectangle.

Top rectangle: 32 * 14 = 448
Stem rectangle: 9 * H
But H is not given.

Unless the "9" in the bottom is the height, but it's listed with 11 and 16, which are likely widths.

Perhaps the 9 is the width of the stem, and the height of the stem is the same as the "14", but that would be double-counting.

I recall that in some problems, the number on the side is the height of that part.

For Figure 17, let's assume that the top bar has height 14, and the stem has height S, and from the bottom, the total width is 36, but the top is 32, so the stem is 9 wide, and the top bar is 32 wide, so the overhang on left and right is (32 - 9)/2 = 11.5, but the bottom has 11 and 16, not symmetric.

11 and 16 are different, so not symmetric.

Perhaps the top bar is not centered; maybe it's flush left or right.

Suppose the top bar is flush left, so from x=0 to x=32, y=0 to y=14.
Then the stem is from x=a to x=a+9, y=14 to y=14+S.
Then at the bottom, y=14+S, the width is from x=0 to x=32 for the top part, but the stem is only 9 wide, so the bottom width should be 32, but the labels show 11,9,16, sum 36, so not.

Unless the bottom includes the stem and the extensions.

Perhaps the shape has the top bar 32 wide, and below it, the stem 9 wide, but the bottom of the shape has the stem and also the sides of the top bar are cut, but it's complicated.

Another idea: the "11", "9", "16" are the lengths of the bottom edges, but for a T-shape, the bottom is only the stem, so perhaps it's not a T.

Let's look at the name: "Area of Composite Figures", and the shape is described as having those labels.

Perhaps it's a rectangle 32x14, and then a rectangle 9xH attached at the bottom center, but then the bottom width would be max(32,9) = 32, but the labels show 36, so not.

Unless the attached rectangle is wider, but it's 9 wide.

I think there might be a mistake in my reasoning.

Let's try this: the total area can be calculated as the area of the large rectangle minus the cutouts, but let's define the bounding box.

Suppose the bounding box is 36 wide (11+9+16) and height 14 + H, but H unknown.

Perhaps the "14" is the height of the entire figure, and the top bar is at the top, so the stem height is 14 - H_t, but H_t unknown.

I recall that in some T-shapes, the height of the top bar is given, and the stem height is given by another number, but here only one number.

Perhaps the "9" in the bottom is the height of the stem, and the "11" and "16" are the widths of the left and right arms, but for a T, there are no arms.

Let's search for a different approach.

Notice that 11 + 9 + 16 = 36, and 32 is the top, so perhaps the top is 32, and the bottom is 36, and it's a trapezoid, but then why the stem.

Perhaps the shape is a rectangle 32x14, and then a rectangle 9xK attached at the bottom, but then the bottom width is 32, not 36.

Unless the attached rectangle is not under the center, but offset.

Suppose the top rectangle is 32x14.
Then attached at the bottom, a rectangle of width 9, height K, positioned such that its left end is at x=11, so from x=11 to x=20, then the bottom width is from x=0 to x=32 for the top, but the stem is only from 11 to 20, so at the bottom, the width is still 32, but the labels show 11,9,16, which might be the distances.

Perhaps the 11,9,16 are the lengths along the bottom, but for the area, we can consider that the shape has a constant height except for the stem.

I think I need to assume that the height of the stem is 9, but that's used for width.

Let's calculate the area as 32*14 + 9*9 = 448 + 81 = 529, but why 9 for height.

Perhaps the "9" is used for both, but that doesn't make sense.

Another idea: in the bottom, the "9" is the width of the stem, and the "11" and "16" are the heights of the left and right parts, but that doesn't fit.

Let's look at Figure 18 for comparison.

Perhaps for Figure 17, the top bar is 32 wide, height 14, and the stem is 9 wide, and the height of the stem is the same as the "9" in the bottom, but the "9" is listed with 11 and 16, so likely not.

Perhaps the 11,9,16 are the widths, and the height is uniform, but then it's not a T.

I recall that in some problems, the number on the side is the height, and for the bottom, the numbers are the widths of the segments, but for a T-shape, the bottom should have only one segment for the stem.

Unless the "11" and "16" are not part of the bottom width, but something else.

Perhaps the shape is like a cross or something, but the description says "T-shape".

Let's try to interpret as: the top bar is 32 wide, 14 high.
Then the stem is 9 wide, and its height is such that the total height is 14 + H, but H not given.

Perhaps the "14" is the total height, and the top bar height is H_t, stem height H_s, with H_t + H_s = 14, but two unknowns.

I think I have to guess that the stem height is 9, as it's the only number left.

So area = 32*14 + 9*9 = 448 + 81 = 529

Or perhaps the stem height is 11 or 16, but that seems arbitrary.

Another thought: in the bottom, the "9" is the width of the stem, and the "11" and "16" are the lengths of the left and right overhangs, but for the top, it's 32, so the overhang on left is 11, on right is 16, but 11+9+16=36, while top is 32, so inconsistency.

32 vs 36, difference of 4, so perhaps the top is 32, bottom is 36, and it's a trapezoid with a stem, but complicated.

Perhaps the shape is a rectangle 36x14, and then a rectangle 9xH removed or added, but not.

Let's calculate the area as the average width times height, but not accurate.

I found a possible interpretation: the "11", "9", "16" are the widths of the three vertical strips, but for a T, it's not.

Perhaps it's not a T, but a different shape.

Looking back at the user's initial description, for Figure 17: "32" on top, "14" on right, "11" "9" "16" on bottom.

And in the grid, it's the first of the last row.

Perhaps the 14 is the height of the right side, which for a T-shape, might be the height of the top bar, and the stem height is given by the context of the bottom.

Another idea: the bottom segments 11,9,16 correspond to the widths, and the height is the same for all, but then the top is 32, so not.

Perhaps the top is 32, and the bottom is 36, and the sides are slanted, but then it's a trapezoid, area = (32+36)/2 * H, but H not given.

I think I need to assume that the height is 14 for the main part, and the stem has height 9, so area = 32*14 + 9*9 = 448 + 81 = 529

Or perhaps the stem height is 14, but then it would be large.

Let's move on and come back.

Figure 18:
Complex L-shape.

Labels: top 16, then down 18, then right 34, then down 44, then left 18, then up, then left 16.

So, let's trace.

Start at top-left: go right 16, down 18, right 34, down 44, left 18, up U, left 16, up V.

For it to close, the net displacement.

Horizontally: +16 +34 -18 -16 = 16+34=50, -18-16= -34, so +16, not zero.

Vertically: -18 -44 +U +V = -62 +U+V, set to 0, so U+V=62.

But not helpful.

Perhaps the "up" after left 18 is to the top, but let's assume that the shape is composed of rectangles.

From the drawing, it's like a large rectangle with cuts, but let's split into parts.

Notice that the total width can be calculated: from left to right, the top is 16, then after down 18, it goes right 34, so total width 16+34=50.
Then it goes down 44, then left 18, so at that point, x=50-18=32, then up, then left 16, so to x=32-16=16, then up to start.

So the left side is from x=0 to x=16 for the top, and from x=16 to x=50 for the middle, etc.

So, we can divide into three rectangles:
- Top-left: 16 x 18 = 288
- Middle: 34 x 44 = 1496? But the height may not be 44 for the middle.

After going down 18 from top, then right 34, then down 44, so the middle rectangle is 34 wide, and height 44, but it starts at y=18, so from y=18 to y=18+44=62.
Then it goes left 18, so to x=50-18=32, then up to y=0 or something.

Then from (32,62) it goes up to (32, H), then left to (16,H), then up to (16,0).

So the left part has a rectangle from x=0 to x=16, y=0 to y=18 (already counted), and from y=18 to y=H, x=0 to x=16, but not necessarily.

From (32,62) up to (32,H), then left to (16,H), then up to (16,0).

So the height H must be such that from y=62 to y=H, and then to y=0, so probably H=0, but that doesn't make sense.

Perhaps "up" means to the top level.

Assume that after going left 18 to (32,62), it goes up to (32,0), then left to (16,0), then up to (16,0) — redundant.

So the path is: start (0,0) -> (16,0) -> (16,18) -> (50,18) -> (50,62) -> (32,62) -> (32,0) -> (16,0) -> (0,0) but from (16,0) to (0,0) is left 16, but in the label, after up, it says "left 16", but from (32,0) to (16,0) is left 16, then from (16,0) to (0,0) is another left 16, but the label says "left 16" once.

In the user's description: "16" on top, "18" down, "34" right, "44" down, "18" left, "16" left — so two "left" : first left 18, then left 16.

So from (50,62) left 18 to (32,62), then left 16 to (16,62), then up to (16,0), then left to (0,0)? But not specified.

Probably, from (16,62) up to (16,0), then left to (0,0).

So the shape has:
- From x=0 to x=16, y=0 to y=62: a rectangle 16x62 = 992
- From x=16 to x=50, y=18 to y=62: a rectangle 34x44 = 1496
But they overlap in x=16 to x=16, but at x=16, it's a line, so no area overlap.

The first rectangle is x=0 to 16, y=0 to 62.
The second is x=16 to 50, y=18 to 62.
So together, they cover x=0 to 50, y=0 to 62, but with a missing part: from x=16 to 50, y=0 to 18 is not covered.

In the shape, from (0,0) to (16,0) to (16,18) to (50,18) to (50,62) to (32,62) to (16,62) to (16,0) to (0,0) — from (16,62) to (16,0) is down, but in the path, after left 16 to (16,62), then up? No, typically "up" means increase y, but in coordinates, if y increases down, but usually in math, y increases up, but in drawings, often y increases down.

To avoid confusion, let's define y=0 at top, y increases down.

So start at (0,0) -> right 16 to (16,0) -> down 18 to (16,18) -> right 34 to (50,18) -> down 44 to (50,62) -> left 18 to (32,62) -> left 16 to (16,62) -> up to (16,0) -> left to (0,0).

From (16,62) to (16,0) is up 62 units, then to (0,0) left 16.

So the shape is a polygon with vertices at (0,0), (16,0), (16,18), (50,18), (50,62), (32,62), (16,62), (16,0), (0,0) — but (16,0) is repeated.

From (16,62) to (16,0) to (0,0), so the point (16,0) is visited twice, but it's fine.

So the shape can be divided into:
- Rectangle A: x=0 to 16, y=0 to 62: area 16*62 = 992
- Rectangle B: x=16 to 50, y=18 to 62: area 34*44 = 1496
But rectangle A includes y=0 to 62, x=0 to 16, and rectangle B is x=16 to 50, y=18 to 62, so together they cover the shape, and no overlap since at x=16, it's a line.

The region from x=16 to 50, y=0 to 18 is not included, which is correct for the shape.

So total area = 992 + 1496 = 2488

Calculate: 16*62 = 16*60 + 16*2 = 960 + 32 = 992
34*44 = 34*40 + 34*4 = 1360 + 136 = 1496
Sum 992+1496=2488

Yes.

Figure 19:
U-shape or something.

Labels: left 20, bottom 30, top has 18,6,6.

So, probably a rectangle with a bite in the top.

Full rectangle: 30 * 20 = 600
Bite: width 18, height? The top has segments 6,18,6, sum 30, so the bite is in the middle, width 18, and height H.

The label "6" on the right might be the height of the bite or something.

From the drawing, after the top, it goes down 6 on the right, but for the bite, the depth is given.

Typically, the bite has height 6, as labeled on the side.

So area = 30*20 - 18*6 = 600 - 108 = 492

Figure 20:
Trapezoid or something.

Labels: top 10, right side 28, bottom 24, left side has 12 and a slant.

So, likely a trapezoid with parallel sides 10 and 24, height 28? But the left side has a vertical part of 12, then a slant.

So, it can be split into a rectangle and a triangle.

Rectangle on right: width 10, height 28 → 280
Triangle on left: base 24 - 10 = 14, height 28 - 12 = 16? Because the left side has a vertical drop of 12, then slant to bottom.

So the triangle has base 14,