Math worksheet for calculating the area and perimeter of irregular polygons, featuring eight different shapes with given dimensions.

Let’s solve each problem step by step. We’ll find the area and perimeter for each irregular polygon.

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Problem 1:

Shape is an L-shape made of two rectangles.

We can split it into:
- Left rectangle: 8 cm wide × 10 cm tall → area = 8 × 10 = 80 cm²
- Top right rectangle: (18 - 8) = 10 cm wide × 4 cm tall → area = 10 × 4 = 40 cm²
→ Total Area = 80 + 40 = 120 cm²

Perimeter: Add all outer sides.
Start from bottom left, go clockwise:
- Bottom: 8 cm
- Right side up to notch: 10 - 4 = 6 cm? Wait — better to trace full path.

Actually, let’s list all outer edges:

From bottom-left corner:
- Up 10 cm
- Right 18 cm
- Down 4 cm
- Left 10 cm (because 18 - 8 = 10)
- Down 6 cm (because 10 - 4 = 6)
- Left 8 cm back to start

Wait — that’s not correct tracing. Let me redraw mentally:

The shape has:
- Left vertical: 10 cm
- Top horizontal: 18 cm
- Right top vertical down: 4 cm
- Then horizontal left: 10 cm (since total width is 18, and bottom part is 8, so 18 - 8 = 10)
- Then vertical down: 6 cm (since total height is 10, and we already went down 4, so 10 - 4 = 6)
- Then horizontal left: 8 cm (bottom base)

But wait — when you go left 10 cm after going down 4 cm, then down 6 cm, then left 8 cm — that would overshoot. Actually, the bottom base is only 8 cm, so the inner horizontal should be 10 cm, but then the last segment should connect back.

Better way: Perimeter of such shapes equals perimeter of bounding box if no holes — but here it's indented.

Standard trick: For rectilinear shapes, perimeter = sum of all outer segments.

List all sides in order (clockwise):

Start at bottom-left:
1. Up: 10 cm
2. Right: 18 cm
3. Down: 4 cm
4. Left: 10 cm (this is the indent)
5. Down: 6 cm (remaining height: 10 - 4 = 6)
6. Left: 8 cm (back to start)

Now add: 10 + 18 + 4 + 10 + 6 + 8 = let’s compute:

10+18=28; +4=32; +10=42; +6=48; +8=56 → 56 cm

Check: Another way — imagine extending the inner corner out — the perimeter is same as a 18x10 rectangle minus nothing? No, because indentation adds extra length.

Actually, for any rectilinear polygon with right angles, perimeter = 2*(width + height) if convex, but here it’s concave — so we must count all outer edges.

Our calculation: 10 (left) + 18 (top) + 4 (right top down) + 10 (inner left) + 6 (inner down) + 8 (bottom) = 56 cm. Correct.

✔ Area = 120 cm²
✔ Perimeter = 56 cm

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Problem 2:

U-shaped or inverted U? It’s a rectangle with a bite taken out of the top middle.

Dimensions:
Total width: 4 + 6 + 4 = 14 in
Height: 8.5 in
Indent depth: 2.5 in

Area: Full rectangle minus the missing rectangle.

Full rectangle: 14 in × 8.5 in = 119 in²
Missing rectangle: 6 in × 2.5 in = 15 in²
→ Area = 119 - 15 = 104 in²

Perimeter: Outer boundary plus the two vertical sides of the indent.

Outer perimeter without indent: 2*(14 + 8.5) = 2*22.5 = 45 in
But the indent removes 6 in from top and adds two sides of 2.5 in each → net change: -6 + 2.5 + 2.5 = -1 in? No.

Actually, original top was 14 in continuous. Now it’s broken into three parts: 4, then down 2.5, across 6, up 2.5, then 4. So compared to straight top of 14, we have added two verticals of 2.5 each → so perimeter increases by 2 * 2.5 = 5 in.

Original perimeter (if solid): 2*(14 + 8.5) = 45 in
But now, instead of one top side of 14, we have: 4 + 2.5 + 6 + 2.5 + 4 = 19 in for the top section? That can’t be.

Better: Trace the entire perimeter.

Start bottom-left:
- Right: 14 in (bottom)
- Up: 8.5 in (right side)
- Left: 4 in (top right)
- Down: 2.5 in (into indent)
- Left: 6 in (across indent)
- Up: 2.5 in (out of indent)
- Left: 4 in (top left)
- Down: 8.5 in (left side) — wait, no, we’re already at top left, need to close.

Actually, after going left 4 in on top left, we are at top-left corner, then down 8.5 in to bottom-left.

So sides:
1. Bottom: 14
2. Right: 8.5
3. Top-right horizontal: 4
4. Indent down: 2.5
5. Indent horizontal: 6
6. Indent up: 2.5
7. Top-left horizontal: 4
8. Left: 8.5

Add them: 14 + 8.5 + 4 + 2.5 + 6 + 2.5 + 4 + 8.5

Group: (14) + (8.5 + 8.5) + (4 + 4) + (2.5 + 2.5) + 6 = 14 + 17 + 8 + 5 + 6 = 50 in

Yes: 14+17=31; +8=39; +5=44; +6=50 → 50 in

✔ Area = 104 in²
✔ Perimeter = 50 in

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Problem 3:

L-shape again.

Split into two rectangles:
Option A: Vertical strip on right: 6 in wide × 19 in tall → area = 6×19 = 114 in²
Plus top horizontal: (12 - 6) = 6 in wide × 7 in tall → area = 6×7 = 42 in²
Total area = 114 + 42 = 156 in²

Check: Other way — big rectangle 12x19 = 228, minus missing part? Missing part is below the top-left: width 6, height (19-7)=12 → area 6×12=72 → 228-72=156. Same.

Perimeter: Trace outer edges.

Start bottom-left of whole shape? Better to define coordinates.

Assume bottom-left of large rectangle is origin.

Shape goes:
- From (0,0) to (12,0) to (12,19) to (6,19) to (6,7) to (0,7) to (0,0)? No — looking at diagram:

Diagram shows:
Top: 12 in
Left side: 7 in down, then right 6 in, then down to bottom which is 19 in total height.

So actually:
- Left vertical: 7 in (from top to first turn)
- Then right 6 in
- Then down (19 - 7) = 12 in to bottom
- Then left ? The bottom width isn't given directly.

From diagram: total width at top is 12 in. After going right 6 in from left, then down 12 in, then the bottom part must extend left to make total width... wait, the bottom horizontal is not labeled, but from context, since it's L-shape, the bottom part should be 12 in wide? No.

Look: The vertical part on the right is 19 in tall, and the horizontal part on top is 12 in wide. The "notch" is 6 in wide and starts 7 in down from top.

So the bottom-left part: from left edge, down 19 in, but the horizontal extent at bottom is only up to where the vertical stem is.

Actually, the shape has:
- Top row: 12 in wide, 7 in high
- Below that, on the right: a column 6 in wide, extending down additional 12 in (since 19 - 7 = 12)

So overall, the bottom width is 6 in (only the right part).

To find perimeter, trace:

Start at top-left:
- Right: 12 in
- Down: 7 in (to the notch level)
- Left: 6 in (across the notch? No — according to diagram, after going down 7 in on left, you go right 6 in, then down to bottom.

I think I misread. Diagram says:

Labelled:
- Top: 12 in
- Left side: 7 in (down from top)
- Then from there, right: 6 in
- Then down: to bottom, and total height is 19 in, so this down part is 19 - 7 = 12 in
- Then left: ? The bottom horizontal is not labeled, but since the right part is 6 in wide, and total top is 12 in, the bottom left part must be 12 - 6 = 6 in wide? But that would mean the bottom is also 12 in wide? Confusing.

Perhaps it's better to assume the shape is composed of:
- Rectangle A: 12 in x 7 in (top)
- Rectangle B: 6 in x 12 in (right stem, attached below the right half of rectangle A)

Then the total height is 7 + 12 = 19 in, good.

Width at top: 12 in, at bottom: only 6 in (since rectangle B is 6 in wide).

So perimeter:

Start at bottom-left of rectangle B? Let's start at top-left of whole shape.

Path:
1. Top: right 12 in
2. Down right side: 19 in (full height)
3. Left along bottom: 6 in (width of stem)
4. Up left side of stem: 12 in (height of stem)
5. Left along the "shelf": 6 in (since 12 - 6 = 6, from right end of shelf to left end)
6. Up left side of top rectangle: 7 in — but we're already at the bottom of the top rectangle's left side? Messy.

After step 4: we are at the bottom-left of the stem, which is also the bottom-right of the "missing" part.

From there, we go left 6 in (along the bottom of the top rectangle's left part), then up 7 in to close.

So sides:
- Top: 12
- Right: 19
- Bottom: 6
- Left-up of stem: 12
- Left-horizontal: 6 (this is the inner bottom of the top rectangle)
- Left-up: 7

But the left-up 7 is from y=0 to y=7, but we are at y=12 after coming up the stem? Inconsistency.

Let's use coordinates.

Set point A at top-left: (0,19) — but usually y=0 at bottom. Set y=0 at bottom.

Define:
- Point P1: (0,0) — bottom-left of the stem? Or of the whole shape?

From diagram description:
- The leftmost point is at x=0.
- At y=19 (top), x from 0 to 12.
- At y=7, from x=0 to x=6? No.

Typically in such diagrams:
- The vertical line on the left is 7 in long from top, so from y=19 down to y=12 (if y=0 at bottom).
- Then from (0,12) to (6,12) — right 6 in.
- Then down to (6,0) — down 12 in.
- Then left to (0,0)? But that would make bottom width 6 in, and left side from (0,0) to (0,12) is 12 in, but the label says left side is 7 in — contradiction.

I think the "7 in" is the height of the top-left part, meaning from top down to the notch is 7 in, so if total height is 19 in, then the stem height is 12 in.

And the width of the stem is 6 in, so the bottom is from x=6 to x=12? No.

Let's read the labels carefully from the image description:

For problem 3:
- Top horizontal: 12 in
- Left vertical: 7 in (down from top)
- Then from there, horizontal right: 6 in
- Then vertical down to bottom: and the total height is 19 in, so this down part is 19 - 7 = 12 in
- The bottom horizontal is not labeled, but since the right part is 6 in wide, and the top is 12 in, the bottom must be 6 in wide, aligned to the right.

So the shape has:
- From (0,19) to (12,19) — top
- (12,19) to (12,0) — right side, 19 in
- (12,0) to (6,0) — bottom, 6 in left
- (6,0) to (6,12) — up 12 in (stem left side)
- (6,12) to (0,12) — left 6 in (the "shelf")
- (0,12) to (0,19) — up 7 in (left side)

Yes! That makes sense.

So perimeter segments:
1. (0,19) to (12,19): 12 in
2. (12,19) to (12,0): 19 in
3. (12,0) to (6,0): 6 in
4. (6,0) to (6,12): 12 in
5. (6,12) to (0,12): 6 in
6. (0,12) to (0,19): 7 in

Sum: 12 + 19 + 6 + 12 + 6 + 7 = let's calculate: 12+19=31; +6=37; +12=49; +6=55; +7=62 in

Area: as before, 12*7 + 6*12 = 84 + 72 = 156 in²

✔ Area = 156 in²
✔ Perimeter = 62 in

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Problem 4:

Another L-shape.

Labels:
- Top: 16.8 ft
- Right side: 13.2 ft
- Bottom: 12.4 ft
- Left side has two parts: 8.1 ft and 4.4 ft, with a 5.1 ft horizontal inset.

From diagram: likely, the left side is stepped.

Assume:
- The full height is 8.1 + 4.4 = 12.5 ft? But right side is 13.2 ft — inconsistency.

Perhaps the 8.1 ft is the top-left vertical, then a horizontal right of 5.1 ft, then down 4.4 ft, then right to meet the bottom.

Total width at top: 16.8 ft
At bottom: 12.4 ft
So the difference is 16.8 - 12.4 = 4.4 ft, which might be the width of the left protrusion.

Height: right side 13.2 ft, left side has 8.1 ft down, then after the inset, down 4.4 ft, so total height on left is 8.1 + 4.4 = 12.5 ft, but right is 13.2 ft — not matching.

Perhaps the 13.2 ft is the full height, and the left side is shorter.

Let's interpret based on standard problems.

Commonly, for such shapes, we can split into two rectangles.

Rectangle 1: the main body, say width 12.4 ft, height 13.2 ft? But then the top has extension.

From the labels:
- The top horizontal is 16.8 ft
- The bottom horizontal is 12.4 ft
- The right vertical is 13.2 ft
- On the left, from top down 8.1 ft, then right 5.1 ft, then down 4.4 ft to the bottom level.

So the total height should be 8.1 + 4.4 = 12.5 ft, but the right side is labeled 13.2 ft — discrepancy.

Perhaps the 13.2 ft includes something else.

Maybe the 13.2 ft is the height of the right part, and the left part is shorter.

Let's calculate the height from the left side: 8.1 + 4.4 = 12.5 ft, so perhaps the right side is 13.2 ft, meaning there's a difference.

This is confusing. Perhaps the 13.2 ft is the full height, and the left side's 8.1 ft is from top to the first turn, then after the 5.1 ft right, it goes down 4.4 ft, but 8.1 + 4.4 = 12.5 < 13.2, so maybe the bottom is not at the same level.

Another idea: the 4.4 ft on left is not down to bottom, but the 5.1 ft is horizontal, and then down to bottom, and the total height is 13.2 ft, so the down part after the 5.1 ft is 13.2 - 8.1 = 5.1 ft? But it's labeled 4.4 ft.

I think there might be a typo in my reasoning. Let's look for consistency.

Perhaps the shape is:

- Start at top-left.
- Right 16.8 ft
- Down 13.2 ft (right side)
- Left 12.4 ft (bottom)
- Up ?
- Then right 5.1 ft
- Up 4.4 ft
- Left to close.

From bottom-left, after going left 12.4 ft from bottom-right, we are at bottom-left.
Then up some amount, but the label says on left side, from top down 8.1 ft, then right 5.1 ft, then down 4.4 ft.

So from top-left, down 8.1 ft to a point, then right 5.1 ft, then down 4.4 ft to the bottom level.

So the total height from top to bottom on the left is 8.1 + 4.4 = 12.5 ft.
But the right side is 13.2 ft, so the bottom is not level? That doesn't make sense for a polygon.

Unless the 13.2 ft is not the full height. Perhaps the 13.2 ft is the height of the right rectangle, and the left part is shorter.

Let's assume that the full height is 13.2 ft, and the left side's "8.1 ft" is from top to the first turn, and the "4.4 ft" is from the second turn to the bottom, but 8.1 + 4.4 = 12.5, so perhaps the distance between the turns is not vertical.

I recall that in such worksheets, the numbers are chosen to work out nicely.

Let me try to calculate area by splitting.

Suppose we split into:
- Rectangle A: width 12.4 ft, height 13.2 ft — but then the top has extra.
- Or, the shape can be seen as a large rectangle minus a small rectangle.

Large rectangle: width 16.8 ft, height 13.2 ft — area = 16.8 * 13.2
But then there's a cut-out on the bottom-left.

From the left side, after down 8.1 ft, we go right 5.1 ft, then down 4.4 ft, so the cut-out is a rectangle of width 5.1 ft and height 4.4 ft? But that would be if it's removed, but in this case, it's part of the shape.

Perhaps it's easier to split into two rectangles:

Rectangle 1: the top part, width 16.8 ft, height 8.1 ft — area = 16.8 * 8.1
Rectangle 2: the bottom part, width 12.4 ft, height 4.4 ft — area = 12.4 * 4.4
But then the total height would be 8.1 + 4.4 = 12.5 ft, but the right side is 13.2 ft, so not matching.

Unless the right side's 13.2 ft is a mistake, or perhaps the 4.4 ft is not the height of the bottom rectangle.

Another approach: the difference in width is 16.8 - 12.4 = 4.4 ft, and the left side has a 5.1 ft horizontal, which is larger than 4.4, so perhaps the 5.1 ft is the width of the left protrusion, and the height of the bottom part is 13.2 - 8.1 = 5.1 ft, but it's labeled 4.4 ft.

I think there might be a error in the problem or my understanding. Let's look at the numbers: 8.1, 4.4, 5.1, 12.4, 13.2, 16.8.

Notice that 8.1 + 4.4 = 12.5, and 13.2 - 12.5 = 0.7, not nice.

Perhaps the 13.2 ft is the height of the right part, and the left part's total height is 8.1 + 4.4 = 12.5 ft, but then the bottom is not aligned, which is unlikely.

Let's calculate the perimeter first by tracing.

Assume the shape has vertices at:
- A: top-left (0, h) but set y=0 at bottom.

Set point B at bottom-right: (12.4, 0) — since bottom is 12.4 ft.
Then up to C: (12.4, 13.2) — right side 13.2 ft.
Then left to D: (0, 13.2) — top 16.8 ft? 12.4 to 0 is 12.4, but top is 16.8, so not.

From C (12.4, 13.2) left to E: (12.4 - 16.8, 13.2) = (-4.4, 13.2) — not good.

Perhaps the top is from x=0 to x=16.8 at y=13.2.
Then down to F: (16.8, 0) — but then bottom is from (16.8,0) to (12.4,0)? That would be left 4.4 ft, but the bottom is labeled 12.4 ft, so from x=a to x=b with b-a=12.4.

Assume the bottom is from x=4.4 to x=16.8, so width 12.4 ft.
Then the left side: from (4.4,0) up to (4.4, y1), then right to (4.4 + 5.1, y1) = (9.5, y1), then down to (9.5,0) — but then the height on left is y1, and the label says from top down 8.1 ft, so if top is at y=13.2, then y1 = 13.2 - 8.1 = 5.1 ft.
Then from (9.5,5.1) down to (9.5,0) — distance 5.1 ft, but the label says 4.4 ft — close but not exact.

5.1 vs 4.4 — not match.

Perhaps the 4.4 ft is the height from the turn to the bottom, so if the turn is at y=4.4, then from top y=13.2 down to y=4.4 is 8.8 ft, but labeled 8.1 ft.

I think there might be a typo in the problem or in my interpretation. For the sake of time, let's assume that the total height is 13.2 ft, and the left side's 8.1 ft is from top to the first turn, and the 4.4 ft is from the second turn to the bottom, and the horizontal 5.1 ft is between, and the bottom width is 12.4 ft, top width 16.8 ft.

Then the difference in width is 16.8 - 12.4 = 4.4 ft, which should be the width of the left part that sticks out, but the horizontal is 5.1 ft, so perhaps the 5.1 ft is the width of the inset, not the protrusion.

Let's try this: the shape is like a rectangle with a bite taken out of the bottom-left.

Full rectangle: width 16.8 ft, height 13.2 ft — area = 16.8 * 13.2 = let's calculate: 16.8 * 13 = 218.4, 16.8*0.2=3.36, total 221.76 ft²

Bite: a rectangle of width 5.1 ft and height 4.4 ft — area = 5.1 * 4.4 = 22.44 ft²

Then area of shape = 221.76 - 22.44 = 199.32 ft²

But is the bite at the bottom-left? From the description, after down 8.1 ft from top, we go right 5.1 ft, then down 4.4 ft, so if we start at top-left, down 8.1 ft, then right 5.1 ft, then down 4.4 ft to bottom, so the bite is not removed; it's part of the shape.

In this case, the shape includes the area under the 5.1 ft horizontal, so it's not a bite; it's an extension.

Perhaps it's better to split into:

- Rectangle 1: from x=0 to x=16.8, y=8.1 to y=13.2 — height 5.1 ft? 13.2 - 8.1 = 5.1 ft, width 16.8 ft — area = 16.8 * 5.1
- Rectangle 2: from x=0 to x=5.1, y=0 to y=8.1 — width 5.1 ft, height 8.1 ft — area = 5.1 * 8.1
- Rectangle 3: from x=5.1 to x=12.4, y=0 to y=4.4 — width 12.4 - 5.1 = 7.3 ft, height 4.4 ft — area = 7.3 * 4.4

But then the right side from y=4.4 to y=13.2 is not covered.

This is messy.

Let's look for online or standard solution, but since I can't, let's assume that the 13.2 ft is the full height, and the left side's 8.1 ft is from top to the first turn, and the 4.4 ft is from the second turn to the bottom, and the horizontal 5.1 ft is the width of the middle part, and the bottom width is 12.4 ft, so the left part from x=0 to x=5.1 is full height 8.1 + 4.4 = 12.5 ft, but 12.5 < 13.2, so perhaps the right part is taller.

Perhaps the 13.2 ft is the height of the right rectangle, and the left rectangle has height 8.1 + 4.4 = 12.5 ft, but then the bottom is not aligned, which is impossible for a simple polygon.

I think there might be a mistake in the problem or in the label. For the sake of completing, let's use the following common method:

For problem 4, area = (16.8 * 8.1) + (12.4 * 4.4) = let's calculate:

16.8 * 8.1 = 16.8*8 = 134.4, 16.8*0.1=1.68, total 136.08
12.4 * 4.4 = 12.4*4 = 49.6, 12.4*0.4=4.96, total 54.56
Sum 136.08 + 54.56 = 190.64 ft²

But then the height is 8.1 + 4.4 = 12.5 ft, while the right side is 13.2 ft, so perhaps the 13.2 ft is incorrect, or perhaps the 4.4 ft is not the height.

Another idea: the 4.4 ft on left is the height of the bottom part, but the total height is 13.2 ft, so the top part height is 13.2 - 4.4 = 8.8 ft, but labeled 8.1 ft — close.

Perhaps it's 8.8 ft, but written as 8.1 by mistake.

Or perhaps in the diagram, the 8.1 ft is from top to the turn, and the turn is at y=13.2 - 8.1 = 5.1 ft from bottom, then down 4.4 ft to y=0.7 ft, not to bottom.

This is taking too long. Let's move to other problems and come back.

Perhaps for problem 4, the intended split is:

- Large rectangle: 16.8 ft x 13.2 ft = 221.76 ft²
- Minus a rectangle of 5.1 ft x (13.2 - 8.1 - 4.4) = 5.1 x 0.7 = 3.57 ft² — not nice.

I recall that in some worksheets, the numbers are chosen so that calculations are easy.

Let's calculate perimeter by adding all sides as per diagram.

From the diagram description, the sides are:
- Top: 16.8 ft
- Right: 13.2 ft
- Bottom: 12.4 ft
- Left has: from bottom up 4.4 ft, then right 5.1 ft, then up 8.1 ft to top — but that would mean the left side is not straight.

So the left boundary consists of:
- From bottom-left, up 4.4 ft
- Then right 5.1 ft
- Then up 8.1 ft to top-left

So the total left "side" is not a single line.

For perimeter, we need to add all outer edges.

So vertices:
- A: top-left
- B: top-right
- C: bottom-right
- D: bottom-left of the right part? Let's define.

From A (top-left) :
- to B: right 16.8 ft
- to C: down 13.2 ft ( to bottom-right)
- to D: left 12.4 ft ( to a point on the bottom)
- to E: up ?
- to F: left ?
- to A: up 8.1 ft?

From the left side description: from A down 8.1 ft to G, then right 5.1 ft to H, then down 4.4 ft to I, and I is on the bottom, and from I to D is the bottom part.

Since bottom is 12.4 ft, and from C to D is 12.4 ft left, so D is at (16.8 - 12.4, 0) = (4.4, 0) if C is at (16.8,0).

Then from D (4.4,0) up to E, but according to left side, from A (0,13.2) down 8.1 ft to G (0,13.2-8.1)=(0,5.1), then right 5.1 ft to H (5.1,5.1), then down 4.4 ft to I (5.1,5.1-4.4)=(5.1,0.7)

Then from I (5.1,0.7) to D (4.4,0) — but that's not horizontal or vertical.

This is not working.

Perhaps the bottom is from x=0 to x=12.4 at y=0, and the right side is from (12.4,0) to (12.4,13.2), then top from (12.4,13.2) to (0,13.2) — but then top is 12.4 ft, not 16.8.

I think I need to accept that for problem 4, the intended solution is:

Area = (16.8 * 8.1) + (12.4 * 4.4) = 136.08 + 54.56 = 190.64 ft²

Perimeter = 16.8 + 13.2 + 12.4 + 8.1 + 5.1 + 4.4 = let's add: 16.8+13.2=30; +12.4=42.4; +8.1=50.5; +5.1=55.6; +4.4=60.0 ft

But this assumes that the left side is composed of 8.1 + 4.4 = 12.5 ft, and the 5.1 ft is horizontal, and the bottom is 12.4 ft, etc.

And the right side is 13.2 ft, which may be a red herring or for another purpose.

Perhaps the 13.2 ft is the height of the right part, and the left part's height is 8.1 + 4.4 = 12.5 ft, but then the bottom is not at the same level, which is unlikely.

For the sake of progress, I'll use:

Area = 190.64 ft²
Perimeter = 60.0 ft

But let's verify with another method.

Suppose we consider the shape as a combination:

- Rectangle 1: 16.8 ft x 8.1 ft = 136.08 ft² (top)
- Rectangle 2: 12.4 ft x 4.4 ft = 54.56 ft² (bottom)
- But they overlap or something? No, if the bottom is below the top, but in this case, the bottom rectangle is only 12.4 ft wide, while the top is 16.8 ft, so the left part of the top extends beyond.

In this case, the total area is indeed 136.08 + 54.56 = 190.64 ft², and the height is 8.1 + 4.4 = 12.5 ft, so perhaps the 13.2 ft is a mistake, or perhaps it's the diagonal or something.

Perhaps the 13.2 ft is the length of the right side, which is correct if the bottom is at y=0, top at y=13.2, but then the left side's 8.1 ft is from y=13.2 to y=5.1, then right 5.1 ft to x=5.1, y=5.1, then down to y=0.7, not to 0.

Then the bottom is from x=5.1, y=0.7 to x=12.4, y=0 — not horizontal.

I think for the purpose of this worksheet, we'll go with the simple addition.

So for problem 4:
Area = 16.8 * 8.1 + 12.4 * 4.4 = 136.08 + 54.56 = 190.64 ft²
Perimeter = 16.8 + 13.2 + 12.4 + 8.1 + 5.1 + 4.4 = 60.0 ft

But 8.1 + 4.4 = 12.5, and 13.2 is given, so perhaps the perimeter should include the full right side 13.2, and the left side is 8.1 + 4.4 = 12.5, but then the horizontal 5.1 is additional.

In the perimeter, we have:
- Top: 16.8
- Right: 13.2
- Bottom: 12.4
- Left-bottom vertical: 4.4
- Middle horizontal: 5.1
- Left-top vertical: 8.1
Sum 16.8+13.2+12.4+4.4+5.1+8.1 = let's calculate: 16.8+13.2=30; 12.4+4.4=16.8; 5.1+8.1=13.2; total 30+16.8=46.8; +13.2=60.0 ft

Yes.

And for area, if we consider the shape as the union of:
- A rectangle 16.8 x 8.1 (top)
- A rectangle 12.4 x 4.4 (bottom)
- But they are not overlapping; the bottom rectangle is below the top, but shifted.

Actually, the bottom rectangle is from x=0 to x=12.4, y=0 to y=4.4
The top rectangle is from x=0 to x=16.8, y=4.4 to y=4.4+8.1=12.5
But then the right side from y=12.5 to y=13.2 is not covered, and the label says right side is 13.2 ft, so perhaps the top rectangle should be from y=13.2-8.1=5.1 to y=13.2, height 8.1 ft, and the bottom from y=0 to y=4.4, height 4.4 ft, so gap from y=4.4 to y=5.1.

Then the area would be 16.8*8.1 + 12.4*4.4 = same as before, 190.64 ft², and the right side from y=0 to y=13.2 is 13.2 ft, good.

The left side: from y=0 to y=4.4: 4.4 ft up, then from y=4.4 to y=5.1: but at x=0, from y=4.4 to y=5.1 is 0.7 ft, but in the diagram, after down 8.1 ft from top, we go right 5.1 ft, so at y=13.2-8.1=5.1, we go right 5.1 ft, so from (0,5.1) to (5.1,5.1), then down to (5.1,0.7) if down 4.4 ft, but 5.1 - 4.4 = 0.7, so to y=0.7, not to 0.

Then from (5.1,0.7) to (12.4,0) — not vertical or horizontal.

This is complicated. Perhaps in the diagram, the "down 4.4 ft" is to the bottom, so y=0, so the turn is at y=4.4, so from top y=13.2 down to y=4.4 is 8.8 ft, but labeled 8.1 ft — so perhaps it's 8.8 ft.

Given the time, I'll proceed with the initial calculation for problem 4 as:

Area = 190.64 ft²
Perimeter = 60.0 ft

But let's check the numbers: 8.1, 4.4, 5.1, 12.4, 13.2, 16.8

Notice that 8.1 + 4.4 = 12.5, and 13.2 - 12.5 = 0.7, and 5.1 - 4.4 = 0.7, so perhaps the horizontal 5.1 ft is at y=4.4, and the down from there is to y=0, but the label says "down 4.4 ft", which would be from y=4.4 to y=0, so 4.4 ft, good, but then from top to y=4.4 is 13.2 - 4.4 = 8.8 ft, but labeled 8.1 ft — so perhaps it's a typo, and it should be 8.8 ft.

If we assume that the left side from top to