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).
[tex]\sf \boxed{\text{Area of the shaded region =$\dfrac{Area \ of \ square - area \ of \ circle}{2}$}}[/tex]
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
[tex]\sf \text{Area of circle = \pi r^2}[/tex] Area of circle = πr²
= 3.14 * 4 * 4
= 50.24 square inches
[tex]\sf \text{Area of shade region = \dfrac{64 - 50.24 }{2}}[/tex]
[tex]\sf \text{Area of the shade region = $\dfrac{64 - 50.24}{2}$}[/tex]
[tex]\sf = \dfrac{13.76}{2}\\\\= 6.88 \ square inches[/tex]
