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How to find the area of a complex shape

How to find the area of a complex shape-example-1

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Answer:

B. 114 cm²

Explanation:

You want to know the area of a complex shape consisting of a triangle and a semicircle.

Areas of Parts

The shape can be divided at the dotted line into two shapes whose areas you have formulas for:

  • semicircle of radius 5 cm
  • triangle with base 15 cm and height 10 cm

Using the formulas for their areas, we find the area of each shape to be ...

A = (1/2)πr² . . . . . . area of semicircle with radius r

A = (1/2)π(5 cm)² = 25/2π cm² ≈ 39 cm²

A = (1/2)bh . . . . . . area of triangle with base b and height h

A = (1/2)(15 cm)(10 cm) = 75 cm²

Total area

The sum of the areas of the parts is ...

total area = semicircle area + triangle area

total area = 39 cm² +75 cm²

total area = 114 cm²

The area of the complex shape is about 114 cm².

User Micrub
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