Let’s solve each problem step by step. We’ll find the area of each shape by breaking them into rectangles, calculating their areas, and adding or subtracting as needed.
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Problem 1:
The shape is an L-shape. We can split it into two rectangles:
- Left rectangle: height = 5m, width = 3m → Area = 5 × 3 =
15 m²
- Bottom right rectangle: length = 15m - 3m = 12m, height = 3m → Area = 12 × 3 =
36 m²
Total area = 15 + 36 =
51 m²
✔ Double-check: Alternatively, think of the whole big rectangle (15m × 5m = 75 m²) minus the missing top-right part (which is 12m wide and 2m tall → 12×2=24). 75 - 24 = 51 m². Same answer!
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Problem 2:
This is also an L-shape, but we can split it differently.
Option: Split into a left rectangle and a bottom-right rectangle.
- Left rectangle: height = 9m, width = 10m - 4m = 6m → Area = 9 × 6 =
54 m²
- Right rectangle: height = 5m, width = 4m → Area = 5 × 4 =
20 m²
Wait — that doesn’t cover the whole shape correctly. Let’s try another way.
Better approach: Think of the full outer rectangle minus the missing corner.
Full rectangle if no cutout: 10m wide × 9m tall = 90 m²
Missing piece: It’s a rectangle on the bottom right. Its width is 4m, and its height is 9m - 5m = 4m → Area = 4 × 4 =
16 m²
So actual area = 90 - 16 =
74 m²
✔ Check by splitting: Top rectangle: 10m × 5m = 50 m²; Bottom-left rectangle: (10-4)=6m wide × (9-5)=4m tall? Wait, no — better to do:
Actually, let’s split vertically:
Left part: 6m wide × 9m tall = 54 m²
Right part: 4m wide × 5m tall = 20 m²
Total = 54 + 20 =
74 m² — yes! Correct.
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Problem 3:
This is a C-shape. We can think of it as a big rectangle with a smaller rectangle cut out from the middle.
Big rectangle: 12m wide × 10m tall =
120 m²
Cut-out rectangle: 5m wide × 6m tall =
30 m²
Area = 120 - 30 =
90 m²
✔ Alternative: Break into three parts — top, bottom, and left side.
Top rectangle: 12m × ? Height? The total height is 10m, and the cutout is 6m tall, so top and bottom together are 10 - 6 = 4m. If symmetric, maybe 2m each? But not specified. Actually, looking at the diagram, the cutout starts from the right side, so:
Actually, better to stick with subtraction method — it’s clearer.
Big rectangle: 12 × 10 = 120
Minus inner rectangle: 5 × 6 = 30
→ 120 - 30 =
90 m²
Yes, correct.
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Final Answer:
1. 51 m²
2. 74 m²
3. 90 m²
Parent Tip: Review the logic above to help your child master the concept of area composite figures worksheet.
