Question

13.) Find the area of the shaded region if the side length of the square is 8 in.

Answer 1

Answer:

Area of shaded region = 6.88 square inches

Step-by-step explanation:

Area of shaded region

  When we subtract the area of the circle from the area of square, we get the area of the 4 corners. When we divide that by 2, we get the area of 2 corners(shaded).
$\sf \boxed{\text{Area of the shaded region = \dfrac{Area \ of \ square - area \ of \ circle}{2} }}$

Square:

Area of square = side *side

                          = 8 * 8

                          = 64 square inches

Circle:

     diameter of the circle = side of the square

                                     d = 8 in

                                      r = 8/2 = 4 in

   $\sf \text{Area of circle = \pi r^2}$  Area of circle = πr²

                            = 3.14 * 4 * 4

                            = 50.24 square inches

$\sf \text{Area of shade region = \dfrac{64 - 50.24 }{2}}$

$\sf \text{Area of the shade region = \dfrac{64 - 50.24}{2} }$

                                       $\sf = \dfrac{13.76}{2}\\\\= 6.88 \ square inches$