Question

Area addition and subtraction

Answer 1

Answer:

3.8 $in^{2}$

Step-by-step explanation:

We are given a square of size 6x6 in. So, area of this square is equal to 6 x 6 = 36 $in^{2}$. Now, the shaded region is $\frac{1}{2}$ x (Area of square - area of semicircles)

The diameter of both semicircles = side of the square = 6in

So, radius (r) = $\frac{1}{2}$ x diameter = $\frac{1}{2}$ x 6 = 3in

And hence, area of semicircle is  = $\frac{1}{2}$ x π$r^{2}$

= $\frac{1}{2}$ x π$3^{2}$

Since, there are two semicircles we multiply above by 2, so area of both semicircles = 2 x $\frac{1}{2}$ π$3^{2}$ = 9π

Area of shaded region =  $\frac{1}{2}$ (36 - 9π) = 3.8628 = 3.8 $in^{2}$ to the nearest tenth.