Let’s solve each compound figure one by one. We’ll break them into rectangles and triangles, find the area of each part, then add them together.
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Figure 1:
This is an L-shaped figure. We can split it into two rectangles:
- Left rectangle: width = 11 ft, height = 32 ft → Area = 11 × 32 =
352 ft²
- Bottom right rectangle: width = (24 - 11) = 13 ft, height = 13 ft → Area = 13 × 13 =
169 ft²
Wait — let me double-check that. Actually, looking again:
The full bottom is 24 ft. The left side goes up 32 ft, but the right part only goes up 13 ft. So if we split vertically at 11 ft from the left:
→ Rectangle A (left): 11 ft wide × 32 ft tall = 352 ft²
→ Rectangle B (right): (24 - 11) = 13 ft wide × 13 ft tall = 169 ft²
Total = 352 + 169 =
521 ft²
✔ Correct.
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Figure 2:
This is a trapezoid? Wait — actually, it looks like a rectangle with a triangle on top? No — looking closely, it’s a rectangle plus a right triangle on the right side.
Actually, better way: It’s a rectangle (8 mm × 4 mm) plus a right triangle on the right.
Base of triangle = (13 - 8) = 5 mm
Height of triangle = 4 mm (same as rectangle)
Area of rectangle = 8 × 4 =
32 mm²
Area of triangle = (base × height)/2 = (5 × 4)/2 =
10 mm²
Total = 32 + 10 =
42 mm²
✔ Correct.
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Figure 3:
This shape has a slanted side. Let’s split it into a rectangle and a triangle.
Bottom part: rectangle 18 cm long, 7 cm high → Area = 18 × 7 =
126 cm²
Top part: triangle on the left. Height of triangle = (15 - 7) = 8 cm
Base of triangle = (18 - 9) = 9 cm? Wait — no.
Actually, look: the top edge is 9 cm, and the total bottom is 18 cm. So the overhang on the left is 18 - 9 = 9 cm. That’s the base of the triangle.
Triangle: base = 9 cm, height = 8 cm → Area = (9 × 8)/2 =
36 cm²
Total = 126 + 36 =
162 cm²
✔ Correct.
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Figure 4:
This is a big rectangle with a triangle cut out? Or added? Looking at the shape: it’s mostly a rectangle, but the top right corner is missing — wait, no, actually it’s a rectangle with a triangle sticking out on top right? Let me see.
Actually, it’s easier to think of it as a large rectangle minus a small triangle? Or split into parts.
Better approach: Split into a rectangle and a triangle.
Main rectangle: 45 in wide, 30 in high → Area = 45 × 30 =
1350 in²
But there’s a triangle on top right. The triangle’s base is 15 in (given), and its height is (50 - 30) = 20 in.
So triangle area = (15 × 20)/2 =
150 in²
Total = 1350 + 150 =
1500 in²
Wait — is the triangle *added* or *cut out*? Looking at the diagram: the shape goes up to 50 in on the right, so yes, the triangle is *on top*, meaning we ADD it.
Yes — correct.
✔ Final check: 1350 + 150 = 1500 in²
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Final Answer:
1. 521 ft²
2. 42 mm²
3. 162 cm²
4. 1500 in²
Parent Tip: Review the logic above to help your child master the concept of compound shapes area worksheet.
