Question

find the area of the shaded region. leave the answer in terms of π and in simplest radical form. the area of the shaded region is \boxed{} sq in. (type an exact answer in terms of π.)

Explanation:

Step1: Calculate square area

$\text{Area}_{\text{square}} = 14^2 = 196$

Step2: Find circle radius

$r = \frac{14}{2} = 7$

Step3: Calculate total circle area

The 4 quarter-circles make 1 full circle:
$\text{Area}_{\text{circle}} = \pi r^2 = \pi(7)^2 = 49\pi$

Step4: Subtract circle from square

$\text{Area}_{\text{shaded}} = 196 - 49\pi$

Answer:

$196 - 49\pi$ sq in