Atriangle is placed in a semicircle with a radius of 9ft, as shown below. find the area of the shaded region.
use the value of 3.14 for pi, and do not round your answer. be sure to include the correct unit in your answer.

The area of the shaded region is 46.17 ft.²

The given parameters are;

The radius of the semicircle, r = 9 ft.

The height of the triangle in the semicircle, h = The radius of the semicircle = 9 ft.

The location of the triangle = Inscribed in the semicircle

The base length of the triangle, b = The diameter of the semicircle

Required parameter = The area of the shaded region

Method;

Find and subtract the area of the triangle from the area of the semicircle

The diameter of the semicircle = 2 × The radius of the semicircle

∴ The diameter of the semicircle = 2 × 9 ft. = 18 ft.

The base length of the triangle, b = The diameter of the semicircle = 18 ft.

The area of the triangle, A = (1/2)·b·h

∴ A = (1/2) × 18 ft. × 9 ft. = 81 ft.²

The area of the semicircle,  = Area of circle/2 = π·r²/2

= π·r²/2

Where;

π = 3.14

∴ = 3.14 · (9 ft.)²/2 = 127.17 ft.²

The area of the shaded region, = - A

∴ = 127.17 ft.² - 81 ft.² = 46.17 ft.²

The area of the shaded region, = 46.17 ft.²

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The height is given as 9 ft. this is also the radius of the circle.

The base of the triangle would be 2 times the radius = 18 feet.

The area of the triangle is 1/2 x 9 x 18 = 81 square feet.

The area of the semi circle is : 1/2 x PI x r^2 = 1/2 x 3.14 x 9^2 = 127.17

The area of the shaded region is the area of the triangle minus the area of the semi circle:

127.17 - 81 = 46.17 square feet.