Question

AcellusFind the area of the yellow region.Round to the nearest tenth.5 ftArea = [? ] ft?

Answer 1

From the given figure,

The length of one side of the square, a=5 ft.

The length of the side of the square is the same as the diameter of the circle.

Hence, the diameter of the circle, D=a=5 ft.

Now, the radius of the circle is,

$r=\frac{D}{2}=\frac{5}{2}=2.5\text{ ft}$

The area of the circle(red region) is,

$\begin{gathered} A_C=\pi r^2 \\ =\pi\times(2.5)^2 \\ =19.63ft^2 \end{gathered}$

The area of the square is,

$\begin{gathered} A_S=a^2 \\ =5^2 \\ =25ft^2 \end{gathered}$

Now, the area of the yellow region can be found as,

$\begin{gathered} A=A_S-A_C \\ =25-19.63\text{ } \\ =5.4ft^2 \end{gathered}$

Therefore, the area of the yellow region is 5.4 sq.ft.