Question

A triangle is placed in a semicircle with a radius of 5 yd, as shown below. Find the area of the shaded region.

Answer 1

Answer:

  14.25 yd^2

Step-by-step explanation:

The triangle area is given by the formula ...

  A = 1/2bh

Here, the base is 10 yd, and the height is 5 yd, so ...

  triangle area = (1/2)(10 yd)(5 yd) = (5 yd)^2 = 25 yd^2

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The semicircle is half the area of a circle with radius 5 yd, so its area is ...

  semicircle area = (1/2)π(5 yd)^2 = 12.5π yd^2 ≈ 39.25 yd^2

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The shaded region is the difference between these areas:

  shaded area = 39.25 yd^2 -25 yd^2 = 14.25 yd^2