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One side of this right triangle is a diameter of the semi-circle. Calculate the area of the entire figure. ​

One side of this right triangle is a diameter of the semi-circle. Calculate the area-example-1

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Answer:

357.08 in²

Explanation:

In the problem, we are given two figures (a semicircle and a triangle). To find the area of the entire figure, we find the area of each figure and add them together.

Given information:

  • The radius of the semicircle: 10 in.
  • The base and height of the triangle: 20in. (base) and 20 in. (height).

Area of a semi circle: 1/2 × r² × π

1/2 × (10)² × π

1/2 × 100 × π

50π ≈ 157.08 in²

Area of a triangle: 1/2 × base × height

1/2 × 20 × 20

1/2 × 400

200 in²

As 10 is the radius of the semicircle, and the diameter of a semicircle is twice the radius, the height of the triangle is 2 × 10, or 20 inches.

Total area: Area of the semicircle + Area of the triangle

157.08 + 200

357.08 in²

User Theo Lenndorff
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