Boost Math Skills With These Engaging Area Of Composite Figures ... - Free Printable

Let's solve each of the compound shape area problems step by step. We'll use π = 3.14 as instructed and round answers to 2 decimal places where needed.

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1) Rectangle with a semicircle on one end

- Rectangle: 12 in (length) × 5 in (height)
- Semicircle: diameter = 5 in → radius = 5/2 = 2.5 in

Area of rectangle = length × height
= 12 × 5 = 60 in²

Area of semicircle = (½) × π × r²
= 0.5 × 3.14 × (2.5)²
= 0.5 × 3.14 × 6.25
= 0.5 × 19.625 = 9.8125 in²

Total Area = 60 + 9.8125 = 69.81 in²

✔ Answer: 69.81 in²

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2) Irregular polygon (trapezoid with a triangle removed)

We can split this into two parts:

- A rectangle on the bottom
- A trapezoid on top? Or better: think of it as a large trapezoid minus a small triangle, or split into simpler shapes.

But let’s break it down:

From the figure:
- Bottom base = 20 ft
- Top has two segments: 7 ft and 8 ft → total top = 15 ft?
Wait, actually, the shape looks like:
- A rectangle of 11 ft height and 15 ft width (since 7+8=15), but the left side is slanted.
Wait — better approach:

Actually, the figure appears to be a trapezoid on the right and a triangle on the left?

Wait — let's re-analyze.

Looking at the diagram:

It has:
- Left side: vertical line of 11 ft
- Bottom: 20 ft
- Top: broken into 7 ft and 8 ft → total 15 ft
- The left edge is straight from bottom-left to top-left, so it's a trapezoid?

Wait — no: the left side is vertical, but the top is not aligned.

Better idea: Split into:
- A rectangle of 11 ft height and 8 ft width (right side)
- A trapezoid on the left: with bases 11 ft and 7 ft? No.

Alternatively, look at it as:
- A rectangle of 11 ft × 8 ft (right part)
- And a trapezoid on the left: with height 11 ft, and parallel sides of 7 ft and ? Wait — not clear.

Wait — actually, the top is 7 ft and 8 ft, but they are connected.

Let’s try another way.

The figure seems to have:
- A horizontal base of 20 ft
- A vertical side of 11 ft on the left
- The top is broken into 7 ft and 8 ft → total 15 ft
- But the left side is vertical, and the top-left corner is cut off?

Wait — perhaps it's a trapezoid with a triangle missing?

No — better: divide into two parts:

1. Rectangle on the right: width = 8 ft, height = 11 ft
→ Area = 8 × 11 = 88 ft²

2. Trapezoid on the left:
- Base1 = 11 ft (left side)
- Base2 = 7 ft (top left segment)
- Height = 11 ft? But that doesn't make sense.

Wait — maybe the top is 7 ft and 8 ft, but the bottom is 20 ft.

Let me reinterpret:

Actually, the figure has:
- Bottom: 20 ft
- Left side: vertical, 11 ft
- Top: two horizontal segments: 7 ft and 8 ft → total 15 ft
- Right side: slanted

So the total width at the bottom is 20 ft, and at the top is 15 ft.

But the left side is vertical, so the right side must be slanted.

This suggests the shape is a trapezoid with:
- Parallel sides: top = 15 ft, bottom = 20 ft
- Height = 11 ft

Yes! Because both top and bottom are horizontal, and left side is vertical, so height is 11 ft.

So it's a trapezoid with:
- Base₁ = 15 ft (top)
- Base₂ = 20 ft (bottom)
- Height = 11 ft

Area of trapezoid = (base₁ + base₂)/2 × height
= (15 + 20)/2 × 11
= 35/2 × 11 = 17.5 × 11 = 192.5 ft²

✔ Answer: 192.50 ft²

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3) Diamond-shaped figure (kite or rhombus)

It's a rhombus or kite with diagonals given:
- Vertical diagonal: 13 yd
- Horizontal diagonal: 19 yd

Area of a rhombus = (d₁ × d₂)/2
= (13 × 19)/2 = 247 / 2 = 123.5 yd²

✔ Answer: 123.50 yd²

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4) L-shaped figure

Break into two rectangles:

- Top rectangle: 16 in × 10 in = 160 in²
- Bottom rectangle: 8 in wide, 6 in high → area = 8 × 6 = 48 in²

Wait — but the total height is 10 in, and the bottom rectangle is only 6 in tall? Then the top rectangle is 10 – 6 = 4 in tall?

Wait — no. Looking at the diagram:

- The entire left side is 10 in
- The right side has a step: 6 in tall, then 8 in wide
- So the top rectangle is 16 in wide and 6 in tall? No.

Wait — the left rectangle is 16 in wide and 10 in tall → area = 16 × 10 = 160 in²

Then there is a missing rectangle on the right-bottom: 8 in wide and 6 in tall? But no — the cutout is on the right side.

Actually, the figure is:
- A large rectangle: 16 in × 10 in → area = 160 in²
- A smaller rectangle removed from the bottom-right: 8 in wide, 6 in tall → area = 8 × 6 = 48 in²

Wait — no, the figure is shaded, and the cutout is not shaded, so we subtract.

But wait — the bottom part is only 8 in wide, and the top part is 16 in wide.

So better: split into two rectangles:

1. Left rectangle: 16 in wide, 6 in tall (bottom part) → area = 16 × 6 = 96 in²
2. Right rectangle: 8 in wide, 4 in tall (top part) → because total height is 10 in, and bottom is 6 in → top is 4 in

Wait — no: the top is 16 in wide, and the bottom is only 8 in wide on the right.

Actually, the top rectangle is 16 in wide and 6 in tall → area = 16 × 6 = 96 in²
Then the bottom rectangle is 8 in wide and 4 in tall (since 10 - 6 = 4) → area = 8 × 4 = 32 in²

Total area = 96 + 32 = 128 in²

✔ Answer: 128.00 in²

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5) Trapezoid-like shape with a parallelogram

This shape has:
- A rectangle on the right: 9 ft wide, 11.6 ft tall → area = 9 × 11.6 = 104.4 ft²
- A parallelogram on the left: base = 9 ft, height = 9 ft → area = base × height = 9 × 9 = 81 ft²

Wait — but the left side is slanted, and the height is 9 ft, so yes.

But the total height is 11.6 ft, and the slanted side goes up 9 ft.

So the shape is:
- A rectangle of 9 ft × 11.6 ft → 104.4 ft²
- Plus a parallelogram of base 9 ft, height 9 ft → 81 ft²

Wait — no: that would double-count.

Actually, the left side is slanted, so the bottom is longer than the top.

Wait — the bottom is 9 ft, and the top is 9 ft, but the left side is slanted upward.

So it's a trapezoid with:
- Two parallel sides: bottom = 9 ft, top = 9 ft? Then it's a rectangle?

No — the left side is slanted, so the top might be shorter.

Wait — looking at the diagram:

- The bottom is 9 ft
- The top is also 9 ft
- The left side is slanted upward from bottom-left to top-left
- The right side is vertical

So it's a trapezoid with:
- One base = 9 ft (bottom)
- Other base = 9 ft (top)
- Height = 11.6 ft

But if both bases are 9 ft, it's a rectangle? But the left side is slanted.

Wait — no: if both bases are equal and parallel, and the sides are not vertical, it's still a parallelogram.

But here, the right side is vertical, and the left side is slanted, so the top and bottom are not parallel?

Wait — no, in standard diagrams, the top and bottom are horizontal, so they are parallel.

So if both are 9 ft, and parallel, and the right side is vertical, then the left side must be vertical too, unless the top is shifted.

Ah — likely the top is shifted.

But the diagram shows:
- Bottom: 9 ft
- Top: 9 ft
- Right side: vertical, 11.6 ft
- Left side: slanted, 9 ft high

So the top is offset to the right.

Thus, the shape is a trapezoid with:
- Parallel sides: bottom = 9 ft, top = 9 ft → same length → so it's a parallelogram
- Height = 11.6 ft
- But since it's a parallelogram, area = base × height = 9 × 11.6 = 104.4 ft²

Wait — but the left side is slanted, and the height is measured perpendicularly.

Yes — the height is 11.6 ft, which is the perpendicular distance between the bases.

So even if it's slanted, area = base × height = 9 × 11.6 = 104.4 ft²

But wait — the left side is labeled 9 ft — is that the height?

No — the vertical dimension is 11.6 ft, and the slanted side is 9 ft long.

But the height is 11.6 ft.

So area = base × height = 9 × 11.6 = 104.4 ft²

✔ Answer: 104.40 ft²

Wait — but the top is 9 ft, and the bottom is 9 ft, so it's a parallelogram with base 9 ft and height 11.6 ft.

Yes.

✔ Answer: 104.40 ft²

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6) Triangle on top of a semicircle

- Semicircle: diameter = 6 yd → radius = 3 yd
- Triangle: base = 6 yd, height = 4 yd

Area of semicircle = (½) × π × r²
= 0.5 × 3.14 × (3)²
= 0.5 × 3.14 × 9 = 0.5 × 28.26 = 14.13 yd²

Area of triangle = (½) × base × height
= 0.5 × 6 × 4 = 12 yd²

Total area = 14.13 + 12 = 26.13 yd²

✔ Answer: 26.13 yd²

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✔ Final Answers:

1) 69.81 in²
2) 192.50 ft²
3) 123.50 yd²
4) 128.00 in²
5) 104.40 ft²
6) 26.13 yd²

Let me know if you'd like a visual explanation or help with any specific shape!