Question

A triangle is placed in a semicircle with a radius of 2 yd, as shown below. Find the area of the shaded region. Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

`A_s=2.28yd^2`

Explanation:

From the question we are told that:

Radius
`r=2yd`

Pie
`\pi=3.14`

Generally the equation for Area of the shaded part
`(A_s)` is mathematically given by

`A_s=Area\ of\ semi-circle(A_c)-Area\ of\ triangle(A_t)`

Generally the equation for Area of semi-circle is mathematically given by

`A_c=(1)/(2)\pi r^2`

`A_c=(1)/(2)*(3.14) (2)^2`

`A_c=6.28yd^2`

Generally the equation for Area of triangle is mathematically given by

`A_t=(1)/(2) base*height`

`A_t=(1)/(2) (2+2)*2`

`A_t=4yd^2`

Therefore Area of the shaded part
`(A_s)`

`A_s=A_c-A_t`

`A_s=6.28yd^2-4yd^2`

`A_s=2.28yd^2`