Chapter 10.4, Problem 45E

To determine

To calculate the Area.

Answer to Problem 45E

27 in²

Explanation of Solution

Given Information: Side = $7\frac{3}{4}$ in and Radius = $3\frac{1}{4}$ in

Formula Used:Area of circle = $\pi \times r^2$ , Area of Square = ${(Side)}^2$ , $\pi =\frac{22}{7}$

Calculation:

Diameter = d, Radius = r.

Now, Radius = $3\frac{1}{4}$ in = $\frac{13}{4}$ in

Side = $7\frac{3}{4}$ in = $\frac{31}{4}$ in

Area of base that not in circle = Area of Square -Area of Circle

Area of base that not in circle = ${(Side)}^2-\pi \times r^2$

Put values of Side and Radius to find area.

Area of base that not in circle = ${\left(\frac{31}{4}\right)}^2-\pi \times {\left(\frac{13}{4}\right)}^2$ in²

So,

Area of base that not in circle = $\left(\frac{961}{16}\right)-\pi \times {\left(\frac{169}{16}\right)}^{}$ in²

Now, $\pi =3.14$

Put the value of $\pi$ to find the area

Area of base that not in circle = $\left(\frac{961}{16}\right)-3.14\times {\left(\frac{169}{16}\right)}^{}$ in²

Area of base that not in circle = $60.06-3.14\times 10.56$ in²

So,

Area of base that not in circle = $60.06-33.15$ in²

Hence,

Area of base that not in circle = 26.91 in²

Nearest Area of base that not in circle = 27 in²