Question

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

Use the value 3.14 forn, and do not round your answer. Be sure to include the correct unit in your answer.
is yd please help

Answer 1

14.25 yd^2

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

__

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

__

The shaded region is the difference between these areas:

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