Here are the step-by-step solutions for each problem on the worksheet.
1) Trapezoid
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Formula: Area = $\frac{(base_1 + base_2)}{2} \times height$
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Values: Base 1 = 14 in, Base 2 = 7 in, Height = 14 in.
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Calculation:
* Add bases: $14 + 7 = 21$
* Divide by 2: $21 / 2 = 10.5$
* Multiply by height: $10.5 \times 14 = 147$
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Area: 147 sq in
2) Semicircle on top of a Square
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Square Area: Side $\times$ Side = $18 \times 18 = 324$ sq cm.
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Semicircle Area:
* Diameter is 18, so Radius ($r$) is 9.
* Full Circle Area = $\pi \times r^2 = 3.14 \times 9^2 = 3.14 \times 81 = 254.34$.
* Half Circle Area = $254.34 / 2 = 127.17$.
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Total Area: $324 + 127.17 = 451.17$.
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Rounding: Round to one decimal place $\rightarrow$ 451.2.
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Area: 451.2 sq cm
3) Semicircle on top of a Rectangle
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Rectangle Area: Length $\times$ Width = $20 \times 15 = 300$ sq yd.
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Semicircle Area:
* Diameter is 6, so Radius ($r$) is 3.
* Full Circle Area = $3.14 \times 3^2 = 3.14 \times 9 = 28.26$.
* Half Circle Area = $28.26 / 2 = 14.13$.
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Total Area: $300 + 14.13 = 314.13$.
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Rounding: Round to one decimal place $\rightarrow$ 314.1.
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Area: 314.1 sq yd
4) Triangle on top of a Semicircle
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Triangle Area: $\frac{1}{2} \times base \times height$.
* Base = 8 m, Height = 12 m.
* Area = $0.5 \times 8 \times 12 = 48$ sq m.
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Semicircle Area:
* Diameter is 8, so Radius ($r$) is 4.
* Full Circle Area = $3.14 \times 4^2 = 3.14 \times 16 = 50.24$.
* Half Circle Area = $50.24 / 2 = 25.12$.
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Total Area: $48 + 25.12 = 73.12$.
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Rounding: Round to one decimal place $\rightarrow$ 73.1.
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Area: 73.1 sq m
5) T-Shape (Two Rectangles)
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Top Rectangle: $12 \text{ in} \times 12 \text{ in} = 144$ sq in.
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Bottom Rectangle: The total width is 20 in. The height is 12 in. Area = $20 \times 12 = 240$ sq in.
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Total Area: $144 + 240 = 384$.
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Area: 384 sq in
6) Rectangle plus Triangle
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Rectangle Area: $20 \text{ cm} \times 20 \text{ cm} = 400$ sq cm.
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Triangle Area:
* Base = 20 cm (same as the side of the rectangle).
* Height = 10 cm.
* Area = $0.5 \times 20 \times 10 = 100$ sq cm.
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Total Area: $400 + 100 = 500$.
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Area: 500 sq cm
7) Triangle plus Semicircle
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Triangle Area:
* Base = 6 ft, Height = 13 ft.
* Area = $0.5 \times 6 \times 13 = 39$ sq ft.
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Semicircle Area:
* Diameter is 6, so Radius ($r$) is 3.
* Full Circle Area = $3.14 \times 3^2 = 28.26$.
* Half Circle Area = $28.26 / 2 = 14.13$.
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Total Area: $39 + 14.13 = 53.13$.
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Rounding: Round to one decimal place $\rightarrow$ 53.1.
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Area: 53.1 sq ft
8) House Shape (Triangle on Rectangle)
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Rectangle Area: Width = 6 yd, Height = 6 yd. Area = $6 \times 6 = 36$ sq yd.
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Triangle Area:
* Base = 6 yd.
* Total height is 9 yd, rectangle height is 6 yd, so triangle height is $9 - 6 = 3$ yd.
* Area = $0.5 \times 6 \times 3 = 9$ sq yd.
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Total Area: $36 + 9 = 45$.
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Area: 45 sq yd
9) L-Shape (Split into two rectangles)
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Method: Split the shape vertically into a left rectangle and a right rectangle.
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Left Rectangle:
* Width = 10 ft.
* Height = 11 ft.
* Area = $10 \times 11 = 110$ sq ft.
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Right Rectangle:
* Width = 8 ft.
* Height = 8 ft.
* Area = $8 \times 8 = 64$ sq ft.
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Total Area: $110 + 64 = 174$.
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Area: 174 sq ft
Final Answer:
1) 147 sq in
2) 451.2 sq cm
3) 314.1 sq yd
4) 73.1 sq m
5) 384 sq in
6) 500 sq cm
7) 53.1 sq ft
8) 45 sq yd
9) 174 sq ft
Parent Tip: Review the logic above to help your child master the concept of area of combined shapes worksheet.
