Question

A triangle is placed in a semicircle with a radius of 7 cm, as shown below. Find the area of the shaded region.Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

First, we have to find the area of the semicircle :

Area of a semicircle =( π radius^2)/2

Replacing with the values given:

A (semicircle) = (3.14 x 7 ^2 ) /2 = 76.93 cm2

Then, find the area of the triangle:

the triangle is formed by 2 right triangles:

Area of a right triangle = 1/2 x base x height

base = 7cm

height =7cm

Replacing with the values:

A (right triangle) = 1/2 x 7 x7 = 24.5 cm2

Since there are 2 right triangles:

Total triangle area = 24.5+24.5 = 49 cm2

Finally, we have to subtract the total area of the triangle to the area of the semicircle:

76.93-49= 27.93 cm2