Question

What is the area of the shaded portion of the circle?

(5π – 11.6) ft2
(5π – 5.8) ft2
(25π – 11.6) ft2
(25π – 5.8) ft2

Answer 1

A

Step-by-step explanation: i did the test and review

Answer 2

The first option is the correct one, the area of the shaded portion of the circle is

[/tex](5 \pi -11.6)ft^2[/tex]

Explanation:

Let us first consider the triangle + the shadow.

The full area of the circle is the radius squared times pi, so

A=
`(5 ft)^2 \cdot \pi \\25 ft^2 \cdot \pi`

Since
`(72^(\circ))/(360^(\circ))=(1)/(5)`, the area of the triangle + the shaded area is one fifth of the area of the whole circle, thus

`A_1=(1)/(5)25 ft^2 \cdot \pi\\ =5 ft^2 \cdot \pi`

If we want to know the area of the shaded part of the circle, we must subtract the area of the triangle from
`A_1`.

The area of the triangle is given by

`A_(triangle)=(1)/(2)\cdot (2.9+2.9)ft \cdot 4 ft\\= 11.6 ft^2`

Thus the area of the shaded portion of the circle is

`A_1-A_(triangle)=5 \pi ft^2-11.6ft^2\\= (5 \pi -11.6)ft^2`