Math worksheet for calculating the area of compound shapes with various geometric figures.

Let’s solve each compound shape one by one. We’ll break each figure into simpler shapes (like rectangles, triangles, semicircles), find their areas, and add or subtract as needed. Remember:
- Area of rectangle = length × width
- Area of triangle = ½ × base × height
- Area of circle = πr² → so semicircle = ½πr²
- Use π ≈ 3.14 if needed
- Round to one decimal place if necessary

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Problem 1:
Shape is a trapezoid with parallel sides 14 in and 7 in, height 14 in? Wait — actually, looking at the diagram: it’s a right trapezoid. The two vertical sides are 14 in and 7 in, and the bottom base is 14 in. So we can think of it as a rectangle + triangle OR use trapezoid formula.

Trapezoid area = ½ × (sum of parallel sides) × height
Here, parallel sides are 14 in and 7 in, and the distance between them (height) is 14 in? Actually, no — in this orientation, the “height” of the trapezoid is the horizontal side? Let me reorient.

Actually, better to split: imagine a rectangle 7 in high × 14 in wide, and on top of it, a triangle with base 14 in and height (14 - 7) = 7 in.

So:
Rectangle: 14 × 7 = 98 in²
Triangle: ½ × 14 × 7 = 49 in²
Total = 98 + 49 = 147.0 in²

Wait — but let’s check using trapezoid formula:
Area = ½ × (a + b) × h, where a and b are the two parallel sides, and h is the perpendicular distance between them.

In this case, the two parallel sides are the left (14 in) and right (7 in) vertical sides? No — actually, in standard position, the bases are the top and bottom. But here, the figure has a slanted top. Actually, the two parallel sides are the left and right? No — they’re not parallel.

Wait — I think I misread. Looking again: it’s a quadrilateral with:
- Left side: 14 in (vertical)
- Bottom: 14 in (horizontal)
- Right side: 7 in (vertical)
- Top: slanted from top-left to top-right.

So yes, it’s a trapezoid with parallel sides being the left and right? No — those are both vertical, so they ARE parallel! Distance between them is 14 in (the bottom).

So area = ½ × (14 + 7) × 14 = ½ × 21 × 14 = 10.5 × 14 = 147 in² → same as before.

✔ Answer for #1: 147.0 in²

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Problem 2:
Rectangle 18 cm × 18 cm, with a semicircle on top. Diameter of semicircle = 9 cm? Wait — the arrow says "9 cm" across the top of the rectangle, which is also the diameter of the semicircle.

But the rectangle is labeled 18 cm on the side and 18 cm on the bottom. If the semicircle sits on top, its diameter should match the width of the rectangle. But here, the rectangle is 18 cm wide, yet the semicircle is marked as 9 cm diameter? That doesn’t make sense unless... wait, maybe the 9 cm is the radius?

Look: the arrow points to the curved part and says “9 cm”. In diagrams, when an arrow goes from center to edge, it’s radius; if across, it’s diameter. Here, the arrow starts at the center line and goes to the edge — so likely radius = 9 cm.

But then the rectangle is 18 cm wide — that matches because diameter would be 18 cm. Yes! So radius = 9 cm.

So:
Rectangle: 18 cm × 18 cm = 324 cm²
Semicircle: ½ × π × r² = ½ × 3.14 × 81 = 1.57 × 81 = let's compute:
3.14 × 81 = 254.34 → half is 127.17 cm²

Total = 324 + 127.17 = 451.17 → round to one decimal: 451.2 cm²

Wait — but the problem says “round your answer to one decimal place if necessary.” Since 451.17 rounds to 451.2, yes.

✔ Answer for #2: 451.2 cm²

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Problem 3:
Rectangle 20 yd × 15 yd, with a semicircle on top. Semicircle diameter = ? Arrow says “6 yd” — again, from center to edge? Or across?

Looking: the arrow is drawn from the center of the top side to the edge of the semicircle — so that’s radius = 6 yd. Then diameter = 12 yd. But the rectangle is 20 yd wide — so the semicircle is only on part of the top? That seems odd.

Wait — perhaps the 6 yd is the diameter? Let me check the diagram description. It says “6 yd” with an arrow pointing to the arc — typically, if it’s across the flat side, it’s diameter. But in many worksheets, if it’s written inside the semicircle with an arrow spanning the diameter, it’s diameter.

Actually, re-examining: in problem 2, “9 cm” was likely radius because rectangle was 18 cm wide. Here, rectangle is 20 yd wide, and semicircle is centered? But 6 yd doesn't divide evenly.

Perhaps the 6 yd is the radius? Then diameter = 12 yd, and it’s placed on top of the 20 yd rectangle — meaning there’s space on sides? But the diagram probably intends the semicircle to span the whole top. Maybe it’s a typo? Or perhaps I misread.

Another possibility: the “6 yd” is the diameter. Let’s assume that, because otherwise it doesn’t fit. If diameter = 6 yd, then radius = 3 yd.

Then:
Rectangle: 20 × 15 = 300 yd²
Semicircle: ½ × π × 3² = ½ × 3.14 × 9 = 1.57 × 9 = 14.13 yd²
Total = 300 + 14.13 = 314.13 → 314.1 yd²

But why would the semicircle be smaller than the rectangle? Maybe it’s correct. Perhaps the diagram shows the semicircle sitting on top with diameter equal to the width? But 6 ≠ 20.

Wait — look back at problem 2: rectangle 18x18, semicircle with “9 cm” — which matched radius since 9*2=18. Here, if rectangle is 20 yd wide, and semicircle has “6 yd”, it might be radius, so diameter 12 yd, and it’s centered, leaving 4 yd on each side? But the problem doesn’t specify, and usually in such problems, the semicircle spans the entire top.

I think there might be a mistake in my assumption. Let me check online or standard problems — but since I can’t, I’ll go with what makes sense.

Alternative interpretation: in problem 3, the “6 yd” is the radius, and the rectangle is 20 yd wide, but the semicircle is only over a portion? But that complicates things.

Perhaps the 6 yd is the diameter, and the rectangle width is not related — but that doesn’t make sense.

Another idea: maybe the “6 yd” is the radius, and the rectangle is 12 yd wide? But it says 20 yd.

I think I need to proceed with the given numbers. Let’s assume the semicircle has diameter 6 yd (so radius 3 yd), and it’s attached to the top of the rectangle, even though the rectangle is wider. Perhaps it’s centered, and we just calculate the area as is.

So:
Rectangle: 20 * 15 = 300
Semicircle: 0.5 * pi * 3^2 = 0.5 * 3.14 * 9 = 14.13
Total: 314.13 → 314.1 yd²

But let’s double-check with another approach. Perhaps the 6 yd is the radius, and the rectangle is 12 yd wide? But the label says 20 yd.

I recall that in some diagrams, the number inside the semicircle with an arrow to the curve is the radius. In problem 2, it was 9 cm for a 18 cm wide rectangle, so radius 9, diameter 18 — perfect match. Here, if rectangle is 20 yd wide, and semicircle has radius 6 yd, diameter 12 yd, then it doesn't match. Unless the 20 yd is not the width? The label "20 yd" is on the bottom, so it is the width.

Perhaps it's a different configuration. Another thought: maybe the semicircle is on the side? But the diagram shows it on top.

I think there might be an error in the problem or my reading. To resolve, let's look at problem 4 for comparison.

Problem 4: teardrop shape — triangle on top of semicircle. Triangle height 12 m, base 8 m? And semicircle with radius 8 m? Wait, it says "8 m" with arrow to the curve, and "12 m" height of triangle.

For problem 3, I'll assume that the "6 yd" is the radius, and the rectangle is 20 yd wide, but the semicircle is only over a 12 yd section? But that's not specified.

Perhaps the 6 yd is the diameter. Let me calculate both ways.

If radius = 6 yd, diameter = 12 yd, then semicircle area = 0.5 * pi * 36 = 56.52 yd², rectangle 300, total 356.52 → 356.5 yd²

If diameter = 6 yd, radius = 3 yd, semicircle = 14.13, total 314.13 → 314.1 yd²

Which one is more likely? In problem 2, "9 cm" was radius for 18 cm width. Here, if "6 yd" is radius, then for consistency, the rectangle should be 12 yd wide, but it's 20 yd. So perhaps it's diameter.

Maybe the 6 yd is the radius, and the 20 yd is a red herring? No.

Another idea: perhaps the semicircle is not on the top of the rectangle, but the rectangle is 20 yd by 15 yd, and the semicircle is attached to the 15 yd side? But the diagram shows it on the 20 yd side.

I think I have to make a decision. Let's look at the answer choices or typical problems. Since this is a worksheet, likely the semicircle spans the width, so diameter = 20 yd, but it's labeled 6 yd — that doesn't work.

Unless the "6 yd" is something else. Perhaps it's the height of the semicircle, but that's radius.

I recall that in some diagrams, the number is the radius. For example, in problem 7, "6 ft" is likely radius.

To avoid delay, I'll assume for problem 3 that the "6 yd" is the radius, and the rectangle is 20 yd wide, but the semicircle is centered, so we still calculate the area of the semicircle as is, and add to rectangle. So radius 6 yd.

So:
Semicircle area = 0.5 * π * 6^2 = 0.5 * 3.14 * 36 = 1.57 * 36 = 56.52 yd²
Rectangle = 20 * 15 = 300 yd²
Total = 356.52 → 356.5 yd²

And for problem 2, it was consistent: radius 9 cm for 18 cm width.

In problem 3, if radius is 6 yd, diameter 12 yd, but rectangle is 20 yd, so perhaps the semicircle is not spanning the whole width, but the problem doesn't say to adjust, so we just add the areas as given.

So I'll go with that.

✔ Answer for #3: 356.5 yd²

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Problem 4:
Teardrop shape: triangle on top of semicircle.
Triangle: base = 8 m, height = 12 m
Semicircle: radius = 8 m (since "8 m" with arrow to curve, and it's the same as the base of the triangle, so diameter = 8 m? Wait, if radius is 8 m, diameter is 16 m, but the triangle base is 8 m — mismatch.

Look: the triangle has base 8 m, and the semicircle is below it, with the same base. So the diameter of the semicircle should be 8 m, so radius = 4 m.

But the label says "8 m" with an arrow to the curve — if it's from center to edge, it's radius, but then diameter would be 16 m, while triangle base is 8 m — doesn't match.

Perhaps the "8 m" is the diameter. In many diagrams, when it's written inside the semicircle with an arrow across, it's diameter.

Assume that the "8 m" is the diameter of the semicircle, so radius = 4 m.

Then:
Triangle area = ½ × base × height = ½ × 8 × 12 = 48 m²
Semicircle area = ½ × π × r² = ½ × 3.14 × 16 = 1.57 × 16 = 25.12 m²
Total = 48 + 25.12 = 73.12 → 73.1 m²

If "8 m" is radius, then semicircle area = 0.5 * pi * 64 = 100.48, triangle 48, total 148.48, but then the base of the triangle is 8 m, while semicircle diameter is 16 m — doesn't align, so unlikely.

So diameter = 8 m, radius = 4 m.

✔ Answer for #4: 73.1 m²

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Problem 5:
L-shaped figure. Can be divided into two rectangles.

One way: bottom rectangle 20 in × 12 in, and top rectangle 12 in × 12 in? Let's see dimensions.

The figure has overall width 20 in, height on right is 12 in, on left is 12+12=24 in? Labels: left side has 12 in (top part) and 12 in (bottom part)? No.

From diagram:
- Total width: 20 in
- On the right, height is 12 in
- On the left, there's a protrusion: from bottom to top of protrusion is 12 in, and the protrusion width is 12 in? The label "12 in" is on the top of the protrusion, and "12 in" on the side.

Actually, it's like a large rectangle minus a small rectangle, or add two rectangles.

Option 1:
- Bottom rectangle: 20 in wide × 12 in high = 240 in²
- Top rectangle: 12 in wide × 12 in high = 144 in² (since the protrusion is 12 in wide and 12 in tall)
But is the top rectangle sitting on the left part? Yes, so total area = 240 + 144 = 384 in²

Option 2: large rectangle 20 in × 24 in = 480 in², minus the missing part on the right top: which is 8 in wide (20-12) and 12 in high, so 96 in², then 480 - 96 = 384 in² — same.

So ✔ Answer for #5: 384.0 in²

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Problem 6:
Pentagon-like shape: rectangle plus triangle on the right.

Rectangle: 20 cm × 20 cm? Width 20 cm, height 20 cm? But on the right, there's a triangle with base 10 cm and height 20 cm? Let's see.

The figure has:
- Left part: rectangle 20 cm wide × 20 cm high
- Right part: triangle attached to the right side, with base 10 cm (horizontal) and height 20 cm (same as rectangle height)

So area = rectangle + triangle = (20 × 20) + (½ × 10 × 20) = 400 + 100 = 500 cm²

Is the triangle's height 20 cm? Yes, since it's attached to the full height.

✔ Answer for #6: 500.0 cm²

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Problem 7:
Right triangle on top of semicircle. Triangle legs 13 ft and ? Base of triangle is the diameter of the semicircle.

Labels: triangle has height 13 ft (vertical leg), and the base is the diameter of the semicircle, which is labeled "6 ft" — but "6 ft" with arrow to the curve, so likely radius = 6 ft, so diameter = 12 ft.

Then:
Triangle area = ½ × base × height = ½ × 12 × 13 = 78 ft²
Semicircle area = ½ × π × r² = ½ × 3.14 × 36 = 56.52 ft²
Total = 78 + 56.52 = 134.52 → 134.5 ft²

If "6 ft" is diameter, then radius = 3 ft, semicircle = 0.5*pi*9=14.13, triangle base=6, area=0.5*6*13=39, total=53.13, but then the triangle base is 6 ft, semicircle diameter 6 ft, which matches, but the label "6 ft" with arrow to curve suggests radius.

In problem 4, we assumed "8 m" was diameter for consistency with base. Here, if "6 ft" is radius, diameter 12 ft, triangle base should be 12 ft, but the diagram may show it as such.

To be consistent with problem 4, where we took "8 m" as diameter because it matched the triangle base, here if the triangle base is not labeled, but the semicircle has "6 ft", and if we assume the triangle base equals the diameter, then if "6 ft" is radius, diameter 12 ft, triangle base 12 ft.

But in the diagram, the triangle's base is the same as the semicircle's diameter, so whatever "6 ft" represents, it should be consistent.

Given that in problem 2 and 3, "9 cm" and "6 yd" were likely radii, and in problem 4, "8 m" was diameter, it's inconsistent.

For problem 7, let's assume "6 ft" is the radius, as the arrow points to the curve from the center.

So radius = 6 ft, diameter = 12 ft.

Triangle: base 12 ft, height 13 ft, area = 0.5*12*13 = 78 ft²
Semicircle: 0.5*pi*36 = 56.52 ft²
Total: 134.52 → 134.5 ft²

✔ Answer for #7: 134.5 ft²

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Problem 8:
House-shaped: rectangle with triangle on top.

Rectangle: width 6 yd, height 8 yd? Labels: "6 yd" at bottom, "8 yd" on the side of the rectangle, and "3 yd" on the sides of the triangle? Also "9 yd" for the height of the triangle.

The triangle has height 9 yd, and the base is the same as the rectangle width, 6 yd. But there are "3 yd" labels on the sides — perhaps indicating the overhang or something.

Looking: the rectangle is 6 yd wide, 8 yd high. On top, a triangle with height 9 yd, but the base of the triangle is wider? The "3 yd" might be the extension on each side.

Typically, in such problems, the triangle base is the same as the rectangle width, but here there are "3 yd" on the left and right, suggesting that the triangle extends 3 yd beyond on each side.

So total base of triangle = 6 + 3 + 3 = 12 yd.

Height of triangle = 9 yd.

Rectangle: 6 yd × 8 yd = 48 yd²
Triangle: ½ × 12 × 9 = 54 yd²
Total = 48 + 54 = 102 yd²

The "3 yd" labels are on the sides, likely indicating the overhang.

✔ Answer for #8: 102.0 yd²

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Problem 9:
L-shaped or stepped rectangle. Can be divided into two rectangles.

One way: left rectangle 10 ft wide × 11 ft high, but then the right part is shorter.

Dimensions: total height on left is 11 ft, on right is 8 ft. Widths: left part 10 ft, right part 8 ft, but they overlap? Better to split horizontally or vertically.

Split into:
- Bottom rectangle: width = 10 + 8 = 18 ft, height = 8 ft → area = 18 × 8 = 144 ft²
- Top rectangle: only on the left, width 10 ft, height = 11 - 8 = 3 ft → area = 10 × 3 = 30 ft²
Total = 144 + 30 = 174 ft²

Alternatively, large rectangle 18 ft × 11 ft = 198 ft², minus the missing part on the top right: which is 8 ft wide × 3 ft high = 24 ft², so 198 - 24 = 174 ft² — same.

✔ Answer for #9: 174.0 ft²

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Now, compiling all answers:

1) 147.0 in²
2) 451.2 cm²
3) 356.5 yd² [assuming radius 6 yd]
4) 73.1 m²
5) 384.0 in²
6) 500.0 cm²
7) 134.5 ft²
8) 102.0 yd²
9) 174.0 ft²

For problem 3, I'm still unsure, but based on consistency with problem 2, I'll keep it as 356.5.

Final Answer:
1) 147.0
2) 451.2
3) 356.5
4) 73.1
5) 384.0
6) 500.0
7) 134.5
8) 102.0
9) 174.0