Answer:
38.88in²
Explanation:
Area of shaded region = Area of square - Area of semi circle
First lets find the area of the square and semi circle
Area of square = s²
Where s = side length
Here we have a given side length of 8in
So s = 8
This means area = 8² = 64in²
Area of semicircle = (πr²)/2
Where r = radius
Here, the side length of the square and the diameter of the semicircle is shared meaning they are congruent. This means the diameter of the semicircle = 8in
To convert from diameter to radius we simply divide by 2
So radius = 8 / 2 = 4
Now we have Area = (πr²)/2
==> plug in r = 4 and π = 3.14
Area = (3.14(4)²))/2
==> simplify exponent
Area = (3.14(16))/2
==> multiply 3.14 and 16
Area = 50.24/2
==> simplify division
Area = 25.12in²
Area of shaded region
We now subtract the two areas
Area of shaded region = Area of square - Area of semi circle
Area of square = 64in² and Area of semicircle = 25.12in²
Area of shaded region = 64in² - 25.12in² = 38.88in²