Find the area and perimeter of irregular shapes with this geometry worksheet.

Let’s solve each problem one by one. We’ll find both the area and perimeter for each shape.

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Problem 1: Rectangle (29 in by 6 in)

This is a regular rectangle, so:

- Area = length × width = 29 × 6
- 29 × 6 = (30 × 6) – (1 × 6) = 180 – 6 = 174 sq in

- Perimeter = 2 × (length + width) = 2 × (29 + 6) = 2 × 35 = 70 in

✔ Area: 174 sq in
✔ Perimeter: 70 in

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Problem 2: Rectangle (18 yd by 11 yd)

Again, regular rectangle.

- Area = 18 × 11
- 18 × 10 = 180, plus 18 × 1 = 18 → 180 + 18 = 198 sq yd

- Perimeter = 2 × (18 + 11) = 2 × 29 = 58 yd

✔ Area: 198 sq yd
✔ Perimeter: 58 yd

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Problem 3: L-shaped irregular shape

We can split this into two rectangles.

Top part: 18 yd wide, height? Total top is 37 yd, bottom right is 11 yd → so left side vertical drop is 4 yd. So top rectangle is 18 yd × 4 yd? Wait — let’s look again.

Actually, better to think:

The whole shape can be seen as:

- A big rectangle minus a small rectangle? Or add two parts.

Looking at dimensions:

Left side: 18 yd horizontal, then down 4 yd, then right to make total bottom 37 yd? Wait — labeled:

Top: 37 yd
Left top: 18 yd
Then down 4 yd
Then right to end — that segment must be 37 - 18 = 19 yd? But it says “11 yd” on the right side.

Wait — maybe I misread.

Labeling:

It shows:

Top edge: 37 yd
Left vertical: not given directly
But from left, goes right 18 yd, then down 4 yd, then right to end — and the rightmost vertical is 11 yd.

So actually, the shape has:

- Top rectangle: 18 yd wide, height = ? Let’s call the full height H.

From the right side: the vertical part is 11 yd. From the left, after going down 4 yd, we go right — so the lower part’s height is 4 yd? No.

Better approach: divide into two rectangles.

Rectangle A (left): width 18 yd, height = let’s say h1
Rectangle B (right): width = 37 - 18 = 19 yd? But wait, the label says “11 yd” on the right — that’s probably the height of the right part.

Actually, looking at standard L-shape problems:

Usually, you have:

Total width = 37 yd
Left part width = 18 yd → so right part width = 37 - 18 = 19 yd? But the diagram labels “11 yd” on the right vertical — which likely means the height of the right rectangle is 11 yd.

And the left part goes down 4 yd more than the right? So total height on left = 11 + 4 = 15 yd?

Yes! That makes sense.

So:

- Left rectangle: 18 yd wide × 15 yd high → area = 18 × 15
18×15 = (20×15) - (2×15) = 300 - 30 = 270 sq yd

- Right rectangle: width = 37 - 18 = 19 yd? Wait no — if the right part is only 11 yd tall, and sits on the bottom, then its width should be such that total bottom is 37 yd.

Actually, let's reconstruct:

Imagine the shape:

Start at top-left.

Go right 18 yd → then down 4 yd → then right some amount → then up 11 yd → then left to close.

Wait — the rightmost vertical is labeled 11 yd — meaning from bottom to top of that part is 11 yd.

And the step down is 4 yd — so the left part is taller by 4 yd → so left height = 11 + 4 = 15 yd.

Now, the bottom total length is 37 yd.

The right rectangle (the shorter one) has height 11 yd, and its width? Since the left part is 18 yd wide, and total bottom is 37 yd, then the right part must extend 37 - 18 = 19 yd to the right? But that would mean the right rectangle is 19 yd wide and 11 yd high.

But then the top of the right rectangle is at height 11 yd, while the left goes up to 15 yd — so yes, that matches the 4 yd step.

So:

Area = area of left rect + area of right rect
= (18 × 15) + (19 × 11)

Calculate:

18 × 15 = 270
19 × 11 = 209
Total area = 270 + 209 = 479 sq yd

Now perimeter: walk around the outside.

Start at top-left corner.

→ Right 18 yd
↓ Down 4 yd
→ Right 19 yd (since 37 - 18 = 19)
↑ Up 11 yd
← Left 37 yd (top edge)
↑ Up 4 yd? Wait no — we’re back at start?

Wait, let's trace carefully.

Actually, better to list all outer sides:

Top: 37 yd (full top)

Right side: 11 yd (vertical)

Bottom: 37 yd (full bottom)

Left side: 15 yd (full left height)

But there’s an inner corner — when we go down 4 yd on the left, then right 19 yd, then up 11 yd — so those are internal? No, they are part of the boundary.

Actually, the perimeter includes all outer edges.

So path:

Start at top-left.

1. Move right along top: 37 yd
2. Move down right side: 11 yd
3. Move left along bottom: 37 yd
4. Move up left side: but wait, the left side isn't straight — because there's a notch.

Actually, from bottom-left, we go up 15 yd? But no — because after going up 11 yd on the right, we turn left and go 19 yd, then up 4 yd to meet the top.

I think I messed up.

Standard way for L-shape perimeter: it’s the same as the perimeter of the bounding rectangle if no holes, but here it’s indented.

Actually, for any polygon, perimeter is sum of all outer sides.

Let me define vertices.

Assume coordinates:

Set bottom-left as (0,0)

Then:

- Go right to (37, 0) — bottom edge
- Go up to (37, 11) — right edge
- Go left to (18, 11) — because the step is at x=18? Wait.

If the left part is 18 yd wide, and total width 37, then the "notch" starts at x=18.

From (37,11), go left to (18,11) — that’s 19 yd
Then go up to (18,15) — since left height is 15 yd (11+4) — that’s 4 yd up
Then go left to (0,15) — 18 yd
Then go down to (0,0) — 15 yd

But now we have extra segments.

List all sides:

1. Bottom: (0,0) to (37,0) → 37 yd
2. Right: (37,0) to (37,11) → 11 yd
3. Inner top-right: (37,11) to (18,11) → 19 yd (leftward)
4. Inner vertical: (18,11) to (18,15) → 4 yd (up)
5. Top-left: (18,15) to (0,15) → 18 yd (left)
6. Left: (0,15) to (0,0) → 15 yd (down)

But this counts the inner parts — but in reality, for perimeter, we only want the outer boundary. In this case, the shape is like a rectangle with a bite taken out? No, it's an L-shape, so the inner corner is part of the boundary.

Actually, in an L-shape, all these sides are on the perimeter.

So total perimeter = 37 + 11 + 19 + 4 + 18 + 15

Calculate:

37 + 11 = 48
48 + 19 = 67
67 + 4 = 71
71 + 18 = 89
89 + 15 = 104 yd

But is that correct? Let me verify with another method.

Notice that for such shapes, the perimeter is equal to the perimeter of the smallest rectangle that contains it, because the indentations don't change the total outer path — wait, is that true?

Bounding box: width 37 yd, height 15 yd.

Perimeter of bounding rectangle: 2*(37+15) = 2*52 = 104 yd — same as above!

Why? Because when you have an L-shape without holes, the perimeter equals the perimeter of the bounding rectangle. The "steps" cancel out in terms of total length.

For example, going down 4 yd and then right 19 yd is equivalent to going diagonally, but in Manhattan distance, it adds the same as going around.

In this case, yes, perimeter is 2*(width + height) of the overall bounding box.

Width = 37 yd, height = 15 yd (since left side is 15 yd tall).

So perimeter = 2*(37 + 15) = 2*52 = 104 yd

Area we calculated as 479 sq yd.

But let me confirm area another way.

Total area if full rectangle: 37 * 15 = 555 sq yd

Minus the missing part: the notch is a rectangle of width 19 yd (37-18) and height 4 yd? No.

In our shape, the "missing" part would be if it were full, but it's not missing — it's added differently.

Earlier we did left rect 18x15=270, right rect 19x11=209, total 479.

Full rectangle 37x15=555, but the right part is only 11 yd high, so the part above it is missing? From y=11 to y=15 over width 19 yd — that's a rectangle 19x4=76 sq yd missing.

So area = 555 - 76 = 479 sq yd — yes, matches.

So:

✔ Area: 479 sq yd
✔ Perimeter: 104 yd

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Problem 4: Another L-shape

Dimensions:

Left vertical: 21 in
Bottom: 26 in
Right vertical: 13 in
Top-right horizontal: 11 in

So, similar to before.

Total height on left: 21 in
On right: 13 in → so the step up is 21 - 13 = 8 in? But labeled "11 in" on top-right — that might be the width of the top part.

Let me interpret.

Probably:

- The shape has a left part height 21 in, width? Not given directly.

From the labels:

Top: has a segment labeled 11 in — likely the width of the top rectangle.

Then down 11 in? No, labeled "11 in" vertically on the right? Wait, the diagram shows:

After the top-left, it goes right, then down 11 in, then right to end, then down to bottom.

Standard interpretation:

The figure is composed of:

- A large rectangle on the left: width W, height 21 in
- Attached to the right, a smaller rectangle on the bottom: width X, height 13 in

But total bottom is 26 in.

Also, the top part extends only partway.

From the label "11 in" on the top-right vertical — I think that's the height of the drop.

Assume:

Start at top-left.

Go right some distance — say A yd
Then down 11 in
Then right to end — total bottom is 26 in, so this right segment is 26 - A
Then down to bottom — but the right side is labeled 13 in, which is probably the height from there to bottom.

So the total height on left is 21 in, on right is 13 in, so the difference is 8 in, but we have a drop of 11 in? Inconsistency.

Perhaps the "11 in" is the width of the top part.

Look at common problems.

Another way: the shape can be divided into two rectangles.

Rectangle 1: left part, width = let's call it W1, height = 21 in
Rectangle 2: right part, width = W2, height = 13 in

Total width = W1 + W2 = 26 in? But the bottom is 26 in, and if both are on bottom, yes.

But the top of the left part is higher.

The vertical drop between them is 21 - 13 = 8 in, but the diagram labels "11 in" — perhaps that's the width of the top section.

I think I need to assume based on standard labeling.

In many worksheets, for such a shape:

- The top horizontal segment is labeled, say, 11 in — meaning the width of the upper rectangle.

- Then the vertical drop is given, but here it's not explicitly given; instead, the heights are given.

Let's read the labels as placed:

In problem 4:

- Left side: 21 in (vertical)
- Bottom: 26 in (horizontal)
- Right side: 13 in (vertical)
- And on the top-right, there's a horizontal segment labeled 11 in — but it's written near the top, so likely the width of the top part.

Perhaps the top part is 11 in wide, and the rest is below.

So, the shape is:

- A rectangle on top: 11 in wide, height H1
- Below it, a larger rectangle: width 26 in, height H2

But the left side is 21 in total, so H1 + H2 = 21 in
The right side is 13 in, which is probably H2, since the top part doesn't extend to the right.

If the top part is only 11 in wide, and the bottom is 26 in wide, then on the right, from the bottom up to the start of the top part is H2, and the top part adds H1 on the left.

So total left height = H1 + H2 = 21 in
Right height = H2 = 13 in
So H1 = 21 - 13 = 8 in

Then, the top rectangle is 11 in wide and 8 in high
The bottom rectangle is 26 in wide and 13 in high

But is the bottom rectangle full width? Yes, since bottom is 26 in.

However, the top rectangle is sitting on the left part of the bottom rectangle, so the area is overlap? No, in L-shape, they are adjacent.

Actually, the bottom rectangle is 26 in wide, 13 in high.

On top of the left part of it, we add a rectangle 11 in wide, 8 in high.

So total area = area of bottom rect + area of top rect = (26 × 13) + (11 × 8)

Calculate:

26 × 13 = 26×10 + 26×3 = 260 + 78 = 338
11 × 8 = 88
Total area = 338 + 88 = 426 sq in

Now perimeter.

Bounding box: width 26 in, height 21 in (since left side is 21 in)

Perimeter of bounding rectangle: 2*(26 + 21) = 2*47 = 94 in

Is that correct for L-shape? Similar to before, yes, because the indentation doesn't add extra perimeter; it's compensated.

Verify by tracing:

Start at top-left.

→ Right 11 in (top of small rect)
↓ Down 8 in (to where it meets the big rect)
→ Right 15 in (since 26 - 11 = 15, to end of top level? But at this point, we are at the top of the big rect on the right part)

Actually, after going down 8 in from the top-right of the small rect, we are at the top-left of the right part of the big rect.

Then we go right 15 in to the top-right corner of the big rect? But the big rect is only 13 in high, and we are at height 13 in from bottom? Let's use coordinates.

Set bottom-left as (0,0)

Big rect: from (0,0) to (26,13) — but the small rect is on top of the left part.

Small rect: from (0,13) to (11,21) — since height 8 in, from y=13 to y=21.

So vertices:

- (0,0)
- (26,0)
- (26,13)
- (11,13) [because from x=11 to x=26 at y=13]
- (11,21)
- (0,21)
- back to (0,0)

Now, perimeter is sum of distances between consecutive points.

1. (0,0) to (26,0): 26 in
2. (26,0) to (26,13): 13 in
3. (26,13) to (11,13): 15 in (left)
4. (11,13) to (11,21): 8 in (up)
5. (11,21) to (0,21): 11 in (left)
6. (0,21) to (0,0): 21 in (down)

Sum: 26 + 13 = 39; +15=54; +8=62; +11=73; +21=94 in

Same as bounding box perimeter.

So:

✔ Area: 426 sq in
✔ Perimeter: 94 in

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Problem 5: Small L-shape

Labels:

Left vertical: 7 ft
Bottom: 14 ft
Top-right horizontal: 3 ft
And "7 ft" on the right vertical? Wait, it says "7 ft" twice? Let's see.

Diagram shows:

- Left side: 7 ft
- Bottom: 14 ft
- On the top, after left part, it goes right 3 ft, then down, and the right vertical is labeled 7 ft? But that can't be if left is 7 ft and it's L-shaped.

Probably, the right vertical is shorter.

Standard: likely, the shape has:

- Left rectangle: width W1, height 7 ft
- Right rectangle: width W2, height H2

Total bottom 14 ft.

The top has a segment labeled 3 ft — probably the width of the top part or the step.

Assume the "3 ft" is the width of the protrusion on top.

Commonly, for such a shape:

The total width is 14 ft.

The left part height is 7 ft.

The right part height is less; the difference is made up by the step.

The label "3 ft" is likely the horizontal part of the step.

And "7 ft" on the right might be a mistake or mislabel.

Looking at the text: "7 ft" on left, "14 ft" on bottom, "3 ft" on top-right horizontal, and "7 ft" on the right vertical — but if right vertical is 7 ft, same as left, then it's a rectangle, but it's drawn as L-shape.

Perhaps the "7 ft" on the right is the height of the lower part.

Another possibility: the shape is symmetric or something.

Let's calculate based on typical problems.

Suppose the L-shape has:

- Vertical leg: 7 ft high, width say A
- Horizontal leg: 14 ft long, height B

But they overlap.

From the labels, likely:

The full height on left is 7 ft.

The full width on bottom is 14 ft.

The top has a segment of 3 ft — probably the width of the top rectangle.

Then the right vertical is labeled 7 ft, but that must be the height from bottom to the start of the top part.

Assume that the right part has height H, and the top part has height 7 - H.

But we have "3 ft" as the width of the top part.

Also, the bottom is 14 ft, so the width of the bottom part is 14 ft.

The top part is attached to the left, so its width is 3 ft, and it extends up.

So, the bottom rectangle is 14 ft wide, height H.

The top rectangle is 3 ft wide, height 7 - H.

But what is H? Not given.

Perhaps the "7 ft" on the right is the height of the right part, so H = 7 ft, but then the top part would have height 0, impossible.

I think there's a typo or misreading.

Looking back at the user's image description, for problem 5: "7 ft" on left, "14 ft" on bottom, "3 ft" on the top horizontal segment, and "7 ft" on the right vertical — but in an L-shape, if both verticals are 7 ft, it must be that the top part is inset.

Perhaps the right vertical is 7 ft, but it's from the bottom to the top of the lower part, and the top part is additional.

Let's assume the following based on common problems:

The shape consists of:

- A rectangle on the bottom: 14 ft wide, 4 ft high (for example)
- A rectangle on the left on top: 3 ft wide, 3 ft high, but then total height would be 7 ft.

If bottom height is H, top height is 7 - H, and top width is 3 ft.

But we need another equation.

Notice that the total width is 14 ft, and the top part is 3 ft wide, so the bottom part extends 14 - 3 = 11 ft to the right beyond the top part.

But no height given for bottom.

Perhaps the "7 ft" on the right is the height of the right side, which is the same as the bottom rectangle's height.

So let's set:

Let the height of the bottom rectangle be H.

Then the height of the top rectangle is 7 - H.

The width of the top rectangle is 3 ft.

The width of the bottom rectangle is 14 ft.

Since the top rectangle is on the left, the area is (14 * H) + (3 * (7 - H))

But we have two variables.

Unless H is given.

Perhaps from the diagram, the right vertical is labeled 7 ft, but that can't be if the total height is 7 ft and it's L-shaped.

Another idea: perhaps the "7 ft" on the right is a mistake, and it's supposed to be the height of the lower part.

In many similar problems, for a shape like this, the dimensions are such that the step is clear.

Let's look at problem 6, which is similar.

Problem 6: "7 ft" on left, "10 ft" on bottom, "3 ft" on top-right horizontal, "6 ft" on right vertical.

For problem 6, it's clearer.

For problem 5, perhaps the right vertical is not 7 ft; maybe it's 4 ft or something.

Perhaps "7 ft" is repeated by error.

Let's assume that the right vertical is the height of the lower part, and it's not 7 ft.

But the label says "7 ft".

Perhaps the shape is:

- Left side 7 ft high
- Bottom 14 ft wide
- The top has a 3 ft wide section, and the right side has a vertical of 7 ft, but that would mean the lower part is 7 ft high, and the top part is additional, so total height >7 ft, but left side is labeled 7 ft, contradiction.

I think there might be a mislabel in my understanding.

Let's try to search for standard interpretation.

Perhaps for problem 5, the "7 ft" on the right is the length of the vertical segment on the right, which is part of the lower rectangle.

And the total height on left is 7 ft, so the upper rectangle has height 7 - H, where H is the height of the lower rectangle.

But we need H.

Notice that in the bottom, it's 14 ft, and the top is 3 ft, so the lower rectangle extends 14 - 3 = 11 ft to the right.

But still no height.

Perhaps the "7 ft" on the right is H, the height of the lower rectangle.

So let's assume that.

So for problem 5:

- Lower rectangle: width 14 ft, height 7 ft? But then the upper rectangle would have height 0, impossible.

Unless the upper rectangle is on top, but if lower is 7 ft high, and left side is 7 ft, then no room for upper.

I think the only logical explanation is that the "7 ft" on the right is a typo, and it's meant to be the height of the lower part, say 4 ft or 3 ft.

Perhaps "7 ft" is the total height, and the right vertical is shorter.

Let's look at the numbers.

Another approach: in such problems, the perimeter can be found as 2*(total width + total height) for L-shapes without holes.

Total width = 14 ft, total height = 7 ft, so perimeter = 2*(14+7) = 42 ft.

For area, we need to know the sizes.

Perhaps the "3 ft" is the width of the top part, and the height of the top part is the difference.

But we need the height of the lower part.

Perhaps from the diagram, the right vertical is labeled, but in text it's "7 ft", but maybe it's 4 ft.

Let's check problem 6 for clue.

Problem 6: left 7 ft, bottom 10 ft, top-right horizontal 3 ft, right vertical 6 ft.

For problem 6, likely:

- Total height left: 7 ft
- Right vertical: 6 ft, so the step up is 1 ft? But 7-6=1 ft.

- Top horizontal: 3 ft, so the top rectangle is 3 ft wide, 1 ft high.

- Bottom rectangle: 10 ft wide, 6 ft high.

Then area = (10*6) + (3*1) = 60 + 3 = 63 sq ft

Perimeter = 2*(10 + 7) = 34 ft, or calculate: 10 + 6 + (10-3) + 1 + 3 + 7 = 10+6+7+1+3+7=34 ft.

Yes.

For problem 5, similarly, if right vertical is say H, then top height is 7 - H.

But in problem 5, it's labeled "7 ft" on right, which would make 7 - 7 = 0, impossible.

Perhaps in problem 5, the "7 ft" on the right is the height of the lower part, and the total height is greater, but the left side is labeled 7 ft, which would be inconsistent.

Unless the left side label is for the lower part.

I think there might be a mistake in the problem or my reading.

Perhaps for problem 5, the shape is different.

Another possibility: the "7 ft" on the right is the length of the vertical segment, but it's not the full height.

Let's assume that the right vertical is 4 ft, as a guess, but that's not good.

Perhaps "7 ft" is repeated, and the right vertical is 4 ft or 3 ft.

Let's calculate with the information.

Suppose the lower rectangle has height H, width 14 ft.

Upper rectangle has width 3 ft, height 7 - H.

Then area = 14H + 3(7-H) = 14H + 21 - 3H = 11H + 21

But we don't know H.

Perimeter = 2*(14 + 7) = 42 ft, as before, for any H, as long as it's L-shaped with those outer dimensions.

For area, we need H.

Perhaps from the diagram, the right vertical is labeled, and in text it's "7 ft", but maybe it's "4 ft" or "3 ft".

Looking back at the user's input, for problem 5: "7 ft" on left, "14 ft" on bottom, "3 ft" on the top horizontal, and "7 ft" on the right vertical — but in the context, perhaps the "7 ft" on the right is a mistake, and it's meant to be the height of the lower part, say 4 ft.

Perhaps it's 3 ft.

Let's look at problem 7 and 8 for pattern.

Problem 7: left 8 ft, bottom 32 ft, right vertical 4 ft, and "10 ft" on the bottom-right horizontal.

For problem 7: likely, the right part has height 4 ft, and the left part has height 8 ft, so the step is 4 ft.

The bottom is 32 ft, and the right part has width 10 ft, so the left part has width 32 - 10 = 22 ft.

Then area = left rect 22*8 + right rect 10*4 = 176 + 40 = 216 sq ft

Perimeter = 2*(32 + 8) = 80 ft.

Similarly for problem 5, perhaps the "7 ft" on the right is the height of the right part, but then total height would be max(7,7) =7, but for L-shape, if both are 7, it must be that the top part is not there, or it's a rectangle.

I think for problem 5, it's likely that the right vertical is 4 ft or 3 ft, but since it's labeled 7 ft, perhaps it's a different configuration.

Another idea: perhaps the "7 ft" on the right is the length of the vertical segment on the right, which is the same as the left, but the shape is not L-shaped in the usual way.

Perhaps it's a rectangle with a bite, but the labels suggest otherwise.

Let's assume that for problem 5, the right vertical is 4 ft, as a common number.

Or perhaps from the "3 ft" and "7 ft", the height of the top part is 3 ft, but that doesn't help.

Let's calculate the area as if the lower part height is H, but we need to find H.

Perhaps in the diagram, the right vertical is labeled, and it's 4 ft, but in text it's written as 7 ft by mistake.

To resolve, let's look at problem 6, which is similar and has "6 ft" on right.

For problem 5, perhaps it's 4 ft.

Maybe "7 ft" is the total height, and the right vertical is 3 ft or something.

Let's try to use the fact that in such problems, the area can be calculated if we know the dimensions.

Perhaps for problem 5, the shape is:

- A rectangle 14 ft by 7 ft, but with a rectangle cut out, but the labels suggest addition.

I recall that in some worksheets, for a shape like this, the dimensions are given as the outer and the step.

Let's assume that the "3 ft" is the width of the top part, and the height of the top part is the difference between left and right heights.

But right height is given as 7 ft, same as left, so difference 0.

Unless the "7 ft" on the right is not the height, but the length of the segment.

Perhaps the right vertical segment is 7 ft, but it's from the bottom to the top of the lower part, and the upper part is additional, so total height is 7 + K, but left side is labeled 7 ft, which would be incorrect.

I think there might be a typo in the problem or in my interpretation.

Perhaps for problem 5, the "7 ft" on the right is the height of the lower part, and the left side label "7 ft" is for the lower part, and the upper part is on top, so total height is 7 + M, but then the left side should be labeled as 7 + M, not 7 ft.

This is confusing.

Let's skip and come back.

For problem 6: left 7 ft, bottom 10 ft, top-right horizontal 3 ft, right vertical 6 ft.

As I said earlier:

- Lower rectangle: 10 ft wide, 6 ft high
- Upper rectangle: 3 ft wide, 1 ft high (since 7 - 6 = 1 ft)
- Area = 10*6 + 3*1 = 60 + 3 = 63 sq ft
- Perimeter = 2*(10 + 7) = 34 ft

For problem 5, if we assume that the right vertical is 4 ft, then upper height = 7 - 4 = 3 ft, width 3 ft, so area = 14*4 + 3*3 = 56 + 9 = 65 sq ft, perimeter 2*(14+7) = 42 ft.

But why 4 ft? Not specified.

Perhaps the "7 ft" on the right is a mistake, and it's 4 ft or 3 ft.

Another possibility: in problem 5, the "7 ft" on the right is the length of the vertical segment, but it's the same as the left, and the 3 ft is the horizontal step, but then the shape might be different.

Perhaps the shape is a rectangle 14 ft by 7 ft with a rectangle 11 ft by 3 ft removed or something, but that doesn't match.

Let's calculate the area as the product if it were rectangle, but it's not.

I think for the sake of progress, I'll assume that for problem 5, the right vertical is 4 ft, as a reasonable guess, but that's not accurate.

Perhaps from the diagram, the right vertical is labeled, and in many sources, for similar problems, it's given.

Let's look at problem 8 for comparison.

Problem 8: top 18 in, left 11 in, right 15 in, bottom 8 in.

For problem 8: likely, the shape has:

- Top part: 18 in wide, height H1
- Bottom part: width W2, height 8 in
- Left side 11 in, right side 15 in.

So total height on left 11 in, on right 15 in, so the bottom part is taller on the right.

So perhaps the bottom rectangle is wider on the right.

Assume:

- The bottom rectangle has height 8 in, width W.
- The top rectangle has width 18 in, height H.
- Total left height = H + 8 = 11 in? Then H = 3 in.
- Total right height = 8 in + something, but labeled 15 in, so perhaps the bottom rectangle extends down on the right.

If left height is 11 in, and it's composed of top and bottom, with bottom height 8 in, then top height = 3 in.

Right height is 15 in, which is greater, so the bottom rectangle must extend below on the right.

So the bottom rectangle has height 8 in on the left, but on the right, it may have additional height.

This is complicated.

Perhaps the shape is:

- A rectangle on top: 18 in wide, 3 in high (since 11 - 8 = 3)
- A rectangle on bottom: width say W, height 8 in, but the right side is 15 in, so if the bottom rectangle has height 8 in, and the top is 3 in, total 11 in on left, but on right, if the bottom rectangle is wider, its height is 8 in, but 8 < 15, so not matching.

Unless the "15 in" is the total height on right, so if the bottom rectangle has height H_b, and top has H_t, then on right, H_b = 15 in, on left, H_t + H_b = 11 in, so H_t = 11 - 15 = -4, impossible.

So perhaps the top rectangle is on the left, and the bottom rectangle is full width, but then right height should be the same as bottom height.

I think for problem 8, likely:

- The bottom part has height 8 in, width W.
- The top part has width 18 in, height H.
- On the left, total height = H + 8 = 11 in, so H = 3 in.
- On the right, the height is 15 in, which must be the height of the bottom part alone, so the bottom part has height 15 in on the right, but on the left, it's 8 in? That doesn't make sense for a rectangle.

Perhaps the bottom part is not rectangular; but usually it is.

Another common configuration: the shape is like a staircase.

For problem 8, perhaps:

- From top-left, go right 18 in, then down 3 in (since 11 - 8 = 3? But 11 is left height), then right to end, then down to bottom.

Assume that the left side is 11 in, right side is 15 in, so the difference is 4 in, and the bottom is 8 in, top is 18 in.

Perhaps the shape has a vertical drop on the right.

Let's define:

Let the width of the top part be 18 in.

Then the bottom part has width W.

The height on left is 11 in, on right is 15 in.

So the bottom part must be taller on the right by 4 in.

So perhaps the bottom rectangle has height 8 in on the left, but on the right, it extends down 4 in more, so total height on right 8 + 4 = 12 in, but labeled 15 in, not matching.

15 - 8 = 7, not 4.

Perhaps the 8 in is the height of the bottom part, and the 15 in is the total height on right, so the top part on right has height 15 - 8 = 7 in, but on left, top part has height 11 - 8 = 3 in, so the top part is sloping, but usually it's rectilinear.

I think for rectilinear shapes, the heights are constant per section.

Perhaps for problem 8, the "8 in" is the height of the lower rectangle, "15 in" is the height of the right side, which includes the lower and upper, but on left, "11 in" is the total height, so inconsistency.

Let's calculate the area as the area of the bounding box minus nothing, but it's irregular.

Perhaps use the method of dividing into rectangles.

For problem 8:

Assume that the shape can be divided into two rectangles:

- Rectangle A: left part, width W1, height 11 in
- Rectangle B: right part, width W2, height 15 in

But they overlap or something.

Total width at top is 18 in, at bottom is not given, but the bottom has "8 in" which is likely the height of the bottom part.

Perhaps the bottom part has height 8 in, and spans the full width, but then the right side should be 8 in, not 15 in.

I think I need to make an assumption.

For problem 5, let's assume that the right vertical is 4 ft, as a common number, so upper height = 7 - 4 = 3 ft, width 3 ft, lower width 14 ft, height 4 ft, area = 14*4 + 3*3 = 56 + 9 = 65 sq ft, perimeter 2*(14+7) = 42 ft.

For problem 6, as above, area 63 sq ft, perimeter 34 ft.

For problem 7: left