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-shaped figure. We can split it into two rectangles:
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Rectangle A (left vertical part):
Height = 5m, Width = 3m → Area = 5 × 3 = 15 m²
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Rectangle B (bottom horizontal part):
The total length is 15m, but we already used 3m for the left part, so this rectangle’s width = 15 - 3 = 12m
Height = 3m → Area = 12 × 3 = 36 m²
Total Area = 15 + 36 =
51 m²
✔ Double-check: Another way — imagine a big rectangle 15m long and 5m high = 75 m². Then subtract the missing top-right rectangle: width = 12m, height = 2m (since 5 - 3 = 2) → 12 × 2 = 24 m². So 75 - 24 = 51 m². Same answer!
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Problem 2:
This is also an L-shape, but rotated. Let’s break it into two rectangles:
Option 1: Split vertically.
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Left rectangle: Width = ? Total width is 10m, right part is 4m wide → left part = 10 - 4 = 6m
Height = 9m → Area = 6 × 9 = 54 m²
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Right rectangle: Width = 4m, Height = 5m → Area = 4 × 5 = 20 m²
Total Area = 54 + 20 =
74 m²
✔ Double-check: Big rectangle 10m × 9m = 90 m². Missing bottom-right rectangle: width = 4m, height = 9 - 5 = 4m → 4 × 4 = 16 m². So 90 - 16 = 74 m². Correct!
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Problem 3:
This is a C-shape. Think of it as a big rectangle with a smaller rectangle cut out from the middle.
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Big outer rectangle:
Width = 12m, Height = 10m → Area = 12 × 10 = 120 m²
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Missing inner rectangle (the hole in the C):
Width = 5m, Height = 6m → Area = 5 × 6 = 30 m²
So, actual area = 120 - 30 =
90 m²
✔ Double-check: You could also split the C into three parts: top bar, bottom bar, and left side. But that’s more work. Subtraction method is easier and 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 of composite figures worksheet 6th grade.
