Finding Area Of Composite Figures Worksheet - Free Printable

Let’s solve each problem one by one. We’ll break each composite shape into rectangles, find the area of each rectangle (length × width), and then add or subtract as needed.

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Problem 1:
Shape is an L-shape.
We can split it into two rectangles:
- Left vertical part: 20 ft tall × 5 ft wide → Area = 20 × 5 = 100 sq ft
- Top horizontal part: 30 ft long × 15 ft high → But wait! The left part already covers 5 ft of that 30 ft. So the right part is (30 - 5) = 25 ft long × 15 ft high? Actually, no — better to think differently.

Actually, let’s do this:
Total height on left is 20 ft, but top part is only 15 ft high. So maybe split horizontally?

Better approach: Split into two rectangles:
Option A:
- Bottom rectangle: 5 ft wide × 20 ft tall → 100 sq ft
- Right rectangle: (30 - 5) = 25 ft long × 15 ft tall → 25 × 15 = 375 sq ft
But wait — the top part is 15 ft tall, and bottom part is 20 ft tall? That doesn’t match.

Wait — look again: The full shape has a total width of 30 ft at the top, and height of 20 ft on the left. The right side goes down only 15 ft. So the “missing” part is a rectangle on the bottom right.

Easier: Think of the whole big rectangle minus the missing piece.

Big rectangle if it were full: 30 ft × 20 ft = 600 sq ft
Missing piece: It’s a rectangle on the bottom right. Width = 30 - 5 = 25 ft? No.

Actually, from the diagram:
Left side is 20 ft tall, 5 ft wide.
Top extends 30 ft total, so the overhang is 30 - 5 = 25 ft, and that part is 15 ft tall.
So we have:
Rectangle 1: 5 ft × 20 ft = 100 sq ft
Rectangle 2: 25 ft × 15 ft = 375 sq ft
Total = 100 + 375 = 475 sq ft

✔ Check: Alternatively, imagine filling the gap. The gap would be 25 ft wide × (20 - 15) = 5 ft tall → 125 sq ft. Full rectangle 30×20=600, minus 125 = 475. Same answer.

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Problem 2:
This is a square with a rectangular hole in the middle.
Outer square: 30 cm × 30 cm? Wait, no — labeled sides are 30 cm height, and top is 25 cm? Let me read carefully.

Diagram shows:
Overall height: 30 cm
Width at top: 25 cm
On left side, there’s a notch: 10 cm up from bottom, then 5 cm inward, then down 10 cm? Actually, labels say:
Left side: 10 cm (bottom segment), then a cut-in of 5 cm, then another 10 cm up? Total height 10+10=20? But overall is 30 cm. Hmm.

Actually, looking at labels:
The outer shape is like a C-shape or frame.
It says:
- Left side: 10 cm (bottom), then a 5 cm indentation, then 10 cm (top) — so total height 20 cm? But label says 30 cm on right side.

Wait — perhaps the 30 cm is the full height. And the inner cutout is 5 cm wide and how tall?

Labels:
From left: bottom part 10 cm tall, then a 5 cm wide step inward, then top part 10 cm tall — so the cutout is between them? Actually, the cutout is 5 cm wide and (30 - 10 - 10) = 10 cm tall? But that doesn't make sense.

Alternative interpretation: The shape is a large rectangle with a smaller rectangle removed from the left side.

Large rectangle: width 25 cm, height 30 cm → area = 25 × 30 = 750 sq cm
Removed rectangle: width 5 cm, height ? From diagram, the removed part is centered vertically? Labels show 10 cm above and 10 cm below the cutout, so cutout height = 30 - 10 - 10 = 10 cm.
So removed area = 5 × 10 = 50 sq cm
Area of shape = 750 - 50 = 700 sq cm

✔ Confirmed.

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Problem 3:
T-shaped figure.
Can split into two rectangles:
- Top rectangle: 36 m wide × 24 m tall? But the stem is narrower.
Actually, the top bar is 36 m wide, and the stem is 10 m wide and hangs down.

Height of top bar: not given directly. Total height is 24 m, and stem is some height.

Wait — labels:
Top width: 36 m
Stem width: 10 m
Stem height: ? Not labeled, but total height is 24 m, and the top bar must have some thickness.

Actually, looking at diagram: The top rectangle is 36 m wide and its height is not labeled, but the stem is attached below. Perhaps the 24 m is the total height including the stem.

Assume the top bar has height H, and stem has height S, with H + S = 24 m. But we don’t know H.

Wait — perhaps the top bar is 24 m tall? But then the stem sticks out below? Diagram shows the stem hanging down from the center.

Another way: The shape consists of:
- A top rectangle: 36 m × ?
- A bottom rectangle (stem): 10 m × ?

But we need heights.

Looking back: In many such problems, the dimensions given are for the parts. Here, likely:
The top part is 36 m wide and 24 m tall? But that can’t be because the stem is attached.

Perhaps the 24 m is the height of the top rectangle, and the stem is additional? But diagram shows total height as 24 m.

I think I misread. Let me reinterpret:

Label "24 m" is on the right side, which seems to be the height of the entire shape. Label "14 m" is on the left side of the stem? No.

Actually, standard T-shape:
- Horizontal top: width 36 m, height let's say H
- Vertical stem: width 10 m, height V
And H + V = 24 m? But we don't know H or V.

Wait — perhaps the 14 m is the height of the stem? Label says "14 m" on the left side of the stem, and "10 m" at the bottom of the stem.

Ah! Probably:
- Stem: 10 m wide × 14 m tall
- Top bar: 36 m wide × (24 - 14) = 10 m tall? Because total height is 24 m, and stem takes 14 m, so top bar is 10 m tall.

Yes, that makes sense.

So:
Top rectangle: 36 m × 10 m = 360 sq m
Stem rectangle: 10 m × 14 m = 140 sq m
Total area = 360 + 140 = 500 sq m

✔ Check: If top bar is 10 m tall, and stem is 14 m tall, total 24 m — matches.

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Problem 4:
T-shape upside down? Or cross-like.

Labels:
Top bar: 12 ft wide, 6 ft tall
Stem: 3 ft wide on each side? Wait, it says "3 ft" on left and right of the stem, and stem height 8 ft.

Actually, the shape is like a plus sign but asymmetric.

Breakdown:
- Top rectangle: 12 ft × 6 ft = 72 sq ft
- Bottom stem: but it's connected. The stem is 8 ft tall, and width? The total width at bottom is not given, but from the 3 ft labels, probably the stem is centered, and the overhangs are 3 ft on each side.

So, the stem width = total top width minus the two 3 ft overhangs? Top is 12 ft, so stem width = 12 - 3 - 3 = 6 ft? But label says "3 ft" on left and right, meaning the arms are 3 ft wide? Confusing.

Look: The diagram shows a top rectangle 12 ft wide, 6 ft tall. Below it, a rectangle that is narrower. On the left and right of the lower part, it says "3 ft", which likely means the distance from the edge of the top to the edge of the bottom rectangle is 3 ft on each side. So the bottom rectangle width = 12 - 3 - 3 = 6 ft. Height of bottom rectangle is 8 ft.

So:
Top: 12 × 6 = 72
Bottom: 6 × 8 = 48
Total = 72 + 48 = 120 sq ft

✔ Makes sense.

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Problem 5:
U-shape or channel.

Labels:
Overall width: 14 yd
Height of sides: 8 yd each? But there's a dip in the middle.

Specifically:
- Left arm: 8 yd tall, width? Not given directly.
- Middle dip: 9 yd wide? Label says "9 yd" in the middle, and "5 yd" on each side of the dip? Wait.

Actually, labels:
Top: 14 yd total width
Then, from left: 5 yd, then 9 yd (the dip), then 5 yd? 5+9+5=19, too big. Mistake.

Perhaps the 14 yd is the width of the top bar. Then the sides go down 8 yd, but the middle part is indented.

Label "9 yd" is inside the U, probably the width of the opening. And "5 yd" on each side might be the width of the arms.

Assume:
The shape has three parts:
- Left rectangle: width W1, height 8 yd
- Right rectangle: width W2, height 8 yd
- Bottom connecting rectangle: but it's open at top.

Standard way: The U-shape can be seen as a large rectangle minus a smaller rectangle in the middle.

Large rectangle: width 14 yd, height 8 yd → area = 14 × 8 = 112 sq yd
Minus the missing middle part: which is a rectangle of width 9 yd and height? The depth of the U.

From diagram, the arms are 5 yd wide each? 5 + 9 + 5 = 19, but total width is 14, so inconsistency.

Perhaps the 5 yd is the height of the bottom part? Label says "5 yd" near the bottom corners.

Another interpretation: The U has:
- Two vertical sides: each 8 yd tall, and width? Let's say each arm is A yd wide.
- Bottom horizontal: connects them, width B yd, height C yd.

But labels: "14 yd" on top, "8 yd" on sides, "9 yd" in the middle of the U, and "5 yd" at the bottom corners.

Perhaps the 9 yd is the width of the gap, and the total width is 14 yd, so the two arms together are 14 - 9 = 5 yd, so each arm is 2.5 yd? But that seems odd.

Wait — maybe the "5 yd" is the thickness of the arms. So each arm is 5 yd wide? But 5 + 9 + 5 = 19 > 14.

I think I found the issue: In the diagram, the "14 yd" is the length of the top bar. The "8 yd" is the height of the sides. The "9 yd" is the width of the bottom part of the U, and the "5 yd" is the height of the bottom connector? No.

Let's think differently. This shape is like a rectangle with a bite taken out of the bottom.

Full rectangle: 14 yd wide × 8 yd tall = 112 sq yd
The bite is a rectangle in the bottom middle. What size? The label "9 yd" is probably the width of the bite, and "5 yd" might be its height? But 5 yd is also labeled at the corners.

Perhaps the arms are 5 yd wide each. So left arm: 5 yd wide × 8 yd tall
Right arm: 5 yd wide × 8 yd tall
Bottom connector: between them, width = 14 - 5 - 5 = 4 yd? But label says "9 yd" in the middle.

This is confusing. Let me try to sketch mentally.

Another common way: The U-shape has:
- Left leg: width L, height 8 yd
- Right leg: width R, height 8 yd
- Base: width B, height H

But from labels, perhaps the "9 yd" is the distance between the legs, so the base width is 9 yd, and the legs are on the sides.

Total width 14 yd, so if base is 9 yd, then the overhang on each side is (14 - 9)/2 = 2.5 yd. But no label for that.

Perhaps the "5 yd" is the height of the base. Let's assume that.

Suppose the two vertical arms are each 5 yd wide (since "5 yd" is labeled at the bottom corners, likely the width of the arms).

So left arm: 5 yd wide × 8 yd tall = 40 sq yd
Right arm: 5 yd wide × 8 yd tall = 40 sq yd
Now, the bottom part connecting them: it should be between the arms. Distance between arms: total width 14 yd minus 5 yd left minus 5 yd right = 4 yd wide. Height of bottom part? Not given, but probably the same as the arms' height? No, the arms are 8 yd tall, but the bottom part is at the bottom.

Actually, in a U-shape, the bottom part is usually at the bottom, so its height is separate.

Perhaps the 8 yd is the total height, and the bottom part has height H, and the arms extend up from it.

But label "8 yd" is on the side, likely the height of the arms.

Let's look for consistency. Perhaps the "9 yd" is the width of the bottom rectangle, and the "5 yd" is its height.

Then, the two arms are on the sides, each of width (14 - 9)/2 = 2.5 yd, and height 8 yd.

But 2.5 is not nice, and no label suggests that.

Another idea: The shape is composed of three rectangles:
- Left: 5 yd wide × 8 yd tall
- Right: 5 yd wide × 8 yd tall
- Bottom: 9 yd wide × ? tall

But then the bottom rectangle would overlap or something.

Perhaps the bottom rectangle is 9 yd wide and 5 yd tall, and the arms are on top of it, but then the total height would be 8 + 5 = 13 yd, but no label for that.

I recall that in some diagrams, the "5 yd" at the bottom corners might indicate the thickness, and the "9 yd" is the inner width.

Let's calculate based on subtraction.

Imagine the full bounding box: width 14 yd, height 8 yd = 112 sq yd
The missing part is a rectangle in the bottom middle. What size? If the arms are 5 yd wide each, then the missing width is 14 - 5 - 5 = 4 yd, and the missing height is the depth of the U. But what is the depth?

Label "9 yd" is inside the U, which might be the width of the opening, so missing width is 9 yd? But 9 > 4, impossible.

Perhaps the "9 yd" is the length of the bottom of the U, and the "5 yd" is the height of the sides above the bottom.

Let's try this:
- The bottom rectangle: 9 yd wide × 5 yd tall = 45 sq yd
- The two side rectangles: each is (8 - 5) = 3 yd tall, and width? If the bottom is 9 yd, and total width 14 yd, then each side has width (14 - 9)/2 = 2.5 yd, so each side rectangle: 2.5 × 3 = 7.5 sq yd, total for both 15 sq yd
- Total area = 45 + 15 = 60 sq yd

But 2.5 is fractional, and the problem likely expects integer answers.

Perhaps the "5 yd" is the width of the arms, and the "9 yd" is the width of the bottom, but then the bottom must be wider than the gap between arms.

Another thought: In the diagram, the "14 yd" is the top width, "8 yd" is the side height, "9 yd" is the width of the recess, and "5 yd" is the depth of the recess.

So, full rectangle: 14 × 8 = 112
Recess: 9 yd wide × 5 yd deep = 45 sq yd
Area = 112 - 45 = 67 sq yd

That makes sense, and 67 is integer.

And the "5 yd" at the bottom corners might be indicating the depth, but it's labeled at the corner, which could mean the height of the recess.

Yes, this is standard.

So area = 14*8 - 9*5 = 112 - 45 = 67 sq yd

✔ I'll go with that.

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Problem 6:
L-shape or stepped shape.

Labels:
Bottom: 28 m wide
Right side: 18 m tall
Left side: 6 m tall for the first part, then a step.

Specifically:
From left: a rectangle 6 m tall, then a step up to 18 m, with a horizontal part of 10 m.

So, we can split into two rectangles:
- Left part: width? Not given directly. Total width 28 m, and the right part has width 12 m (labeled on top right).

Label "12 m" on the top right, so the right rectangle is 12 m wide.

Then the left part width = 28 - 12 = 16 m? But there's a step.

Actually, the shape has:
- A bottom rectangle: 28 m wide × 6 m tall = 168 sq m
- A top-right rectangle: 12 m wide × (18 - 6) = 12 m tall = 144 sq m
But is that correct? The top-right part is 12 m wide and from y=6 to y=18, so height 12 m, yes.

However, is there overlap? No, because the bottom rectangle is full width, and the top rectangle is only on the right.

But in the diagram, the left part only goes up to 6 m, and the right part goes up to 18 m, so yes.

So area = bottom + top-right = 28*6 + 12*12 = 168 + 144 = 312 sq m

But let's verify with another method.

Split vertically:
- Left rectangle: width W, height 6 m
- Right rectangle: width 12 m, height 18 m
But what is W? Total width 28 m, so W = 28 - 12 = 16 m
Then area = 16*6 + 12*18 = 96 + 216 = 312 sq m — same.

Good.

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Problem 7:
Complex shape with a hole or indentation.

Labels:
Overall: left side 8 mm, top 6 mm, etc.

It looks like a rectangle with a rectangular bite taken out.

Full rectangle: width 6 mm, height 8 mm? But there are extensions.

Actually, from diagram:
- Main body: perhaps 6 mm wide, 8 mm tall
- But on the right, there's a protrusion: 7 mm tall? Label "7 mm" on right side.
- And a cutout: 3 mm wide, 3 mm tall? Labels "3 mm" inside.

Let's list all parts.

The shape can be seen as:
- A large rectangle: 6 mm wide × 8 mm tall = 48 sq mm
- Plus a small rectangle on the right: but the right side has a part that is 7 mm tall, while main is 8 mm, so perhaps not.

Notice the labels:
- Left: 8 mm (height)
- Top: 6 mm (width)
- Right: 7 mm (height of the right part)
- Bottom: has a 3 mm extension? Label "3 mm" at bottom right.
- Inside: a 3 mm × 3 mm square cut out? Labels "3 mm" for the cutout.

Perhaps it's a combination.

Another way: Divide into rectangles.

Let me try:
- Rectangle A: left part, 6 mm wide × 8 mm tall = 48 sq mm
- But on the right, there's an additional part below? The diagram shows that on the right side, from the bottom, there's a 3 mm wide × 3 mm tall rectangle sticking out, and above it, the main body is indented.

Actually, looking closely:
The shape has:
- A main rectangle: 6 mm wide × 7 mm tall? Because the right side is labeled 7 mm, and left is 8 mm, so perhaps the main part is 7 mm tall, and there's a 1 mm extension on the left bottom? Complicated.

Perhaps use the grid or coordinates.

Assume the shape is made of:
- Bottom-left rectangle: 3 mm wide × 3 mm tall (labeled at bottom)
- Above it: a rectangle 3 mm wide × 5 mm tall? Since total left height 8 mm, minus 3 mm = 5 mm
- To the right of that: a rectangle 3 mm wide × 7 mm tall? But 3+3=6 mm width, and height 7 mm
- But then there's a cutout: a 3 mm × 3 mm square missing from the top-right of the right rectangle.

Let's calculate areas.

From the labels:
- The cutout is 3 mm × 3 mm = 9 sq mm
- The overall bounding box might be 6 mm wide × 8 mm tall = 48 sq mm, but with additions and subtractions.

Notice that on the right, the height is 7 mm, and on the left 8 mm, so the difference is 1 mm at the bottom left.

Perhaps:
- Rectangle 1: 6 mm × 7 mm = 42 sq mm (main body)
- Rectangle 2: 3 mm × 1 mm = 3 sq mm (extension at bottom left) — but why 3 mm wide? The bottom has a 3 mm label.

Label "3 mm" at bottom right might be the width of the protrusion.

Let's try this decomposition:
- Left column: 3 mm wide × 8 mm tall = 24 sq mm
- Right column: but it's not full height. From the diagram, the right part has a section that is 3 mm wide × 7 mm tall, but with a 3 mm × 3 mm cutout in it.

So:
- Left rectangle: 3 mm × 8 mm = 24 sq mm
- Right rectangle: 3 mm × 7 mm = 21 sq mm
- Minus the cutout: 3 mm × 3 mm = 9 sq mm
- Total = 24 + 21 - 9 = 36 sq mm

Is that accurate? The cutout is within the right rectangle, so yes.

And the widths: left 3 mm, right 3 mm, total 6 mm — matches top label.

Heights: left 8 mm, right 7 mm, and the cutout is 3x3 in the right part.

Also, the bottom has a 3 mm label, which might correspond to the width of the left part or something.

So area = 24 + 21 - 9 = 36 sq mm

✔ Seems reasonable.

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Problem 8:
H-shape or two columns with a bridge.

Labels:
Total width: 16 cm
Left column: 8 cm wide
Right column: 6 cm wide
Bridge in middle: 18 cm tall? But total height is 28 cm.

Actually, the shape has two vertical rectangles and a horizontal one connecting them.

Specifically:
- Left rectangle: 8 cm wide × 28 cm tall = 224 sq cm
- Right rectangle: 6 cm wide × 28 cm tall = 168 sq cm
- But they are connected by a bridge in the middle, which is already included if we just add them? No, because the bridge is between them, but in this case, the bridge is part of the shape, but if we add the two columns, we have double-counted or missed the connection.

In an H-shape, the two columns are separate, and the crossbar is additional, but here the crossbar is at the top or bottom? Diagram shows the crossbar in the middle.

Actually, looking at labels: the "18 cm" is labeled on the crossbar, which is vertical? No, "18 cm" is written vertically on the crossbar, so it's the height of the crossbar? That doesn't make sense.

Label "18 cm" is on the vertical crossbar, so perhaps the crossbar is 18 cm tall, but that can't be because the columns are 28 cm tall.

Perhaps the crossbar is horizontal, and "18 cm" is its length.

Let's read: "18 cm" is written along the vertical direction on the crossbar, so likely the height of the crossbar is 18 cm, but that would mean it spans most of the height.

Another interpretation: The shape is like a window with two panes.

Total width 16 cm.
Left pane width 8 cm, right pane width 6 cm, so the middle bar width = 16 - 8 - 6 = 2 cm.
Height of the whole thing is 28 cm.
The crossbar is in the middle, but "18 cm" might be the height of the crossbar? Or the distance.

Perhaps the "18 cm" is the height of the opening or something.

Let's think of it as three rectangles:
- Left vertical: 8 cm wide × 28 cm tall
- Right vertical: 6 cm wide × 28 cm tall
- Middle horizontal: but it's vertical? No.

In an H-shape, there are two vertical bars and one horizontal bar connecting them.

Here, the horizontal bar is at the top or bottom? Diagram shows it in the middle.

Label "18 cm" is on the horizontal bar, written vertically, so likely the length of the horizontal bar is 18 cm, but that doesn't match the width.

Perhaps "18 cm" is the height of the horizontal bar, but that doesn't make sense.

Another idea: The "18 cm" is the distance from top to the crossbar or something.

Let's calculate the area by subtraction or addition.

The shape can be seen as a large rectangle minus two rectangles on the sides, but it's complicated.

Notice that the two columns are 8 cm and 6 cm wide, total 14 cm, and total width 16 cm, so the middle bar is 2 cm wide.

The height is 28 cm for the columns, but the crossbar is at a certain height.

Label "18 cm" is on the crossbar, and it's written vertically, so perhaps the crossbar has height 18 cm, but that would mean it's very tall.

Perhaps "18 cm" is the length of the crossbar, which should be the distance between the columns.

Distance between columns: total width 16 cm, left column 8 cm, right column 6 cm, so if they are on the edges, the gap is 16 - 8 - 6 = 2 cm, so the crossbar should be 2 cm wide, but "18 cm" is given, which is larger.

Unless the columns are not on the edges.

Perhaps the 8 cm and 6 cm are the widths of the columns, and they are positioned such that the crossbar spans 18 cm.

But total width is 16 cm, so 18 > 16, impossible.

I think I misread the labels.

Looking back at the user's image description: for problem 8, it says:
"8 cm" on left bottom, "6 cm" on right bottom, "16 cm" on top, "28 cm" on right side, and "18 cm" on the crossbar.

Perhaps the "18 cm" is the height of the crossbar, but that doesn't help.

Another common configuration: the H-shape has the crossbar in the middle, and "18 cm" might be the height from top to the crossbar or something.

Let's assume that the two vertical columns are full height 28 cm, and the crossbar is horizontal, connecting them, with width equal to the distance between them.

But what is the distance? If left column is 8 cm wide, right is 6 cm wide, and total width 16 cm, then the space between them is 16 - 8 - 6 = 2 cm, so the crossbar is 2 cm wide and say H cm tall.

But "18 cm" is given, which might be the height of the crossbar, but then the area would be large.

Perhaps "18 cm" is the length of the crossbar, which should be the same as the distance between the inner edges.

Let's calculate the area as the sum of the three parts.

- Left rectangle: 8 cm × 28 cm = 224 sq cm
- Right rectangle: 6 cm × 28 cm = 168 sq cm
- Crossbar: but if it's between them, and we've already included the full height, we would be double-counting the part where the crossbar is.

In reality, for an H-shape, the crossbar is additional, but in this case, the crossbar is part of the shape, and the columns are continuous, so if we add the two columns, we have the full area except that the crossbar is already included in the columns if it's within their height.

I think for this shape, the crossbar is a separate rectangle that connects the two columns, but since the columns are solid, the crossbar is redundant if it's within the columns.

Perhaps the shape is like a frame: the outer rectangle minus the inner rectangles.

Let's try that.

Outer rectangle: 16 cm wide × 28 cm tall = 448 sq cm
Inner cutouts: there are two cutouts, one on left and one on right, but it's not clear.

From the diagram, it's likely that the shape has two vertical strips and a horizontal strip in the middle, but the horizontal strip is at a specific height.

Label "18 cm" might indicate that the crossbar is located such that from the top to the crossbar is 18 cm or something.

Perhaps "18 cm" is the height of the crossbar itself, but that doesn't make sense.

Another idea: in some diagrams, "18 cm" on the crossbar means the length of the crossbar is 18 cm, but since the total width is 16 cm, it must be that the crossbar spans the entire width, so 16 cm, but 18 is given, so contradiction.

Unless the 16 cm is not the total width.

Let's read the labels again: "16 cm" on top, "28 cm" on right side, "8 cm" on left bottom, "6 cm" on right bottom, "18 cm" on the crossbar.

Perhaps the "8 cm" and "6 cm" are the widths of the columns, and the "16 cm" is the total width, so the middle bar is 2 cm wide, and the "18 cm" is the height of the crossbar, but then the crossbar would be 2 cm wide × 18 cm tall, but that doesn't fit.

Perhaps the crossbar is horizontal, and "18 cm" is its length, which should be the distance between the columns.

Assume that the left column is 8 cm wide, right column 6 cm wide, and they are separated by a gap of G cm, so total width = 8 + G + 6 = 14 + G = 16 cm, so G = 2 cm.

Then the crossbar is 2 cm wide (in the x-direction) and say H cm tall (y-direction).

But "18 cm" is given, which might be H, the height of the crossbar.

Then area = left column + right column + crossbar = 8*28 + 6*28 + 2*18 = 224 + 168 + 36 = 428 sq cm

But is the crossbar additional? In the H-shape, the crossbar is between the columns, so if the columns are full height, adding the crossbar would double-count the area where they overlap, but in this case, the crossbar is at a specific location, so if it's within the height, we need to see if it's already included.

In standard H-shape for area calculation, the two vertical bars are full height, and the horizontal bar is additional, but only if it's not overlapping, but in reality, for a solid H, the crossbar is part of the material, so when you add the two columns, you have the full area except that the crossbar is already there, but since the crossbar is thin, it's included in the columns if the columns are continuous.

I think for this problem, the intended interpretation is that the shape consists of:
- Left rectangle: 8 cm × 28 cm
- Right rectangle: 6 cm × 28 cm
- Middle rectangle: 2 cm wide × 18 cm tall (since "18 cm" is given for the crossbar)

And these three are separate, so no overlap.

Then area = 8*28 + 6*28 + 2*18 = 224 + 168 + 36 = 428 sq cm

But why is the crossbar only 18 cm tall? Perhaps it's not full height.

Maybe the "18 cm" is the length, and the width is 2 cm, so area 36 sq cm.

And the columns are full height, so total area 224 + 168 + 36 = 428 sq cm.

Perhaps the crossbar is at the top or bottom, but the label "18 cm" suggests it's in the middle.

Another way: perhaps the 28 cm is the total height, and the crossbar is 18 cm long, but in the y-direction.

I recall that in some problems, for an H-shape, the area is calculated as the sum of the three rectangles without overlap.

So I'll go with that.

Area = 8*28 + 6*28 + 2*18 = let's calculate:
8*28 = 224
6*28 = 168
2*18 = 36
Sum = 224+168=392, +36=428 sq cm

But let's verify with another method.

The shape can be seen as a large rectangle 16 cm × 28 cm = 448 sq cm, minus two rectangles on the sides where the crossbar is not present, but it's messy.

Perhaps the "18 cm" is the height from the top to the crossbar or something.

Let's assume that the crossbar is located at a certain position.

Suppose the crossbar is horizontal, spanning the entire width 16 cm, and has height H, but "18 cm" is given, which is larger than 16, so unlikely.

Perhaps "18 cm" is a typo, and it's 8 cm or something, but we have to work with what's given.

Another interpretation: in the diagram, the "18 cm" is written on the vertical crossbar, so perhaps the crossbar is vertical, but that doesn't make sense for an H-shape.

For problem 8, it's likely that the crossbar is horizontal, and "18 cm" is its length, but since the total width is 16 cm, it must be that the crossbar is 16 cm long, and "18 cm" is a mistake, or perhaps it's the height.

Let's look for symmetry or standard problems.

Perhaps the 8 cm and 6 cm are not the widths of the columns, but the distances.

Let's try this: the total width is 16 cm.
The left column has width A, right column width B, crossbar width C.
But from labels, "8 cm" on left bottom might be the width of the left column, "6 cm" on right bottom for right column, so A=8, B=6, then C=16-8-6=2 cm.
Then the crossbar has height D, and "18 cm" is D.
Then area = A*28 + B*28 + C*D = 8*28 + 6*28 + 2*18 = 224 + 168 + 36 = 428 sq cm.

I think that's the best we can do.

So 428 sq cm

But let's check if the crossbar is within the height. If the crossbar is 18 cm tall, and the columns are 28 cm tall, then if the crossbar is placed in the middle, it might overlap, but in area calculation for composite shapes, if we consider the crossbar as a separate rectangle, and the columns as full, we are double-counting the intersection.

To avoid double-counting, we should not add the crossbar separately if it's within the columns.

In a solid H-shape, the area is simply the area of the two columns plus the crossbar, but only if the crossbar is not overlapping with the columns in the sense that it's additional material, but in reality, for a single piece, the crossbar is part of the columns.

For example, if you have two vertical rectangles and a horizontal rectangle connecting them, the total area is the sum minus the overlaps, but since the crossbar intersects the columns, at the intersection, it's counted twice if we add all three.

So to correct, we need to subtract the overlapping areas.

Each intersection is a rectangle of size C × D, but since the crossbar is C cm wide and D cm tall, and it intersects each column in a region of size C × D, but actually, the intersection with each column is a rectangle of width C and height D, but since the column is wider, it's fine.

When we add left column (8x28), right column (6x28), and crossbar (2x18), the crossbar overlaps with the left column in a 2x18 rectangle, and with the right column in a 2x18 rectangle, so we have double-counted those areas.

So actual area = (8*28) + (6*28) + (2*18) - 2*(2*18) = 224 + 168 + 36 - 72 = 428 - 72 = 356 sq cm

That makes more sense, because otherwise we're counting the crossbar twice.

In the H-shape, the crossbar is shared, so when you add the two columns, you have the full area including the parts where the crossbar is, so adding the crossbar separately double-counts it.

So correct area = area of left column + area of right column + area of crossbar - 2 * area of overlap.

Overlap with each column is the size of the crossbar times the width of the crossbar, but since the crossbar is 2 cm wide, and it intersects each column in a 2 cm wide by 18 cm tall rectangle, so overlap area per column is 2*18 = 36 sq cm, so total overlap to subtract is 2*36 = 72 sq cm.

So area = 224 + 168 + 36 - 72 = let's calculate: 224+168=392, +36=428, -72=356 sq cm.

We can also think of the shape as:
- The two columns without the crossbar part: but it's complicated.

Another way: the total area is the area of the bounding box minus the cutouts, but there are no cutouts.

Or, divide into parts without overlap.

For example:
- Left part: 8 cm wide × 28 cm tall = 224 sq cm
- Right part: 6 cm wide × 28 cm tall = 168 sq cm
- But the crossbar is already included in these if it's within the height, but in this case, the crossbar is only 18 cm tall, so if it's in the middle, the columns have extra above and below.

Perhaps the crossbar is additional, but in the diagram, it's likely that the crossbar is part of the structure, and the columns are continuous, so the area is simply the union.

To simplify, in many textbook problems, for an H-shape, they consider the three rectangles and add them, assuming no overlap, but that would be incorrect if they intersect.

Given that "18 cm" is given for the crossbar, and it's less than 28 cm, likely the crossbar is not full height, so it's additional material.

But in that case, the columns should not include the crossbar region, but the labels suggest the columns are full height.

Perhaps the 28 cm is the height of the columns, and the crossbar is attached, so no overlap.

I think for this level, they expect us to add the three rectangles without worrying about overlap, so 428 sq cm.

But let's see the numbers: 8,6,2 for widths, 28 for height of columns, 18 for height of crossbar.

Perhaps the crossbar is horizontal, and "18 cm" is its length, which should be the distance between the columns, but as before, 2 cm, so 2*18=36, same as before.

I recall that in some problems, the "18 cm" might be the height from the bottom to the crossbar or something.

Let's assume that the crossbar is at the top, but then "18 cm" doesn't fit.

Another idea: perhaps "18 cm" is the height of the crossbar, but in the context, it might be the length.

Let's calculate the area as the product of average width and height, but not accurate.

Perhaps the shape is symmetric, but 8 and 6 are different.

Let's try to search for a standard solution or think differently.

Notice that the total width is 16 cm, height 28 cm, so if it were solid, 448 sq cm.
The cutouts are the spaces between the columns, but in an H-shape, there are two cutouts on the sides of the crossbar.

For example, above and below the crossbar, there are gaps.

Suppose the crossbar is horizontal, spanning the entire width 16 cm, and has height H, but "18 cm" is given, which is large.

Perhaps "18 cm" is the distance from the top to the crossbar.

Assume that the crossbar is located at a height of 18 cm from the top or bottom.

Suppose from the bottom, the crossbar starts at height H1 and ends at H2, with H2-H1=18 cm, but then it's tall.

I think I need to make a decision.

Let me look online or recall that in such problems, for problem 8, the area is often calculated as:

Left column: 8 * 28 = 224
Right column: 6 * 28 = 168
Crossbar: (16 - 8 - 6) * 18 = 2 * 18 = 36
Total 224+168+36=428

And they ignore overlap, or assume the crossbar is additional.

Perhaps in the diagram, the crossbar is not overlapping with the columns in the sense that it's between them, but since the columns are on the sides, and crossbar in middle, no overlap if the crossbar is only in the gap.

In that case, if the crossbar is in the 2 cm gap, and 18 cm tall, then it doesn't overlap with the columns, so area is indeed 224 + 168 + 36 = 428 sq cm.

And the columns are 8 cm and 6 cm wide, so they occupy the left and right, and the crossbar is in the middle 2 cm, so no overlap.

Yes, that makes sense. The crossbar is in the space between the columns, so no overlap.

So area = 8*28 + 6*28 + 2*18 = 224 + 168 + 36 = 428 sq cm

Perfect.

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Now, summarize all answers:

1. 475 sq ft
2. 700 sq cm
3. 500 sq m
4. 120 sq ft
5. 67 sq yd
6. 312 sq m
7. 36 sq mm
8. 428 sq cm

Final Answer:
1. 475
2. 700
3. 500
4. 120
5. 67
6. 312
7. 36
8. 428