Question

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

Answer 1

Answer:

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]

Step-by-step 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 $\frac{72^{\circ}}{360^{\circ}}=\frac{1}{5}$, the area of the triangle + the shaded area is one fifth of the area of the whole circle, thus

$A_1=\frac{1}{5}25 ft^2 \cdot \pi\\ =5 ft^2 \cdot \pi$

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

$A_{triangle}=\frac{1}{2}\cdot (2.9+2.9)ft \cdot 4 ft\\= 11.6 ft^2$

Thus the area of the shaded portion of the circle is

$A_1-A_{triangle}=5 \pi ft^2-11.6ft^2\\= (5 \pi -11.6)ft^2$