Answer:
Area of shaded region = 220.16 ft²
Explanation:
The diagram associated with this question is shown in the attached image
Unit in diagram is ft, so I'll use this unit in the answer
We are given that a circle with radius 16 ft is inscribed in a square
We know that the radius of an inscribed circle in a square is equivalent to half the length of the side of the square
This means that:
side length of the square = 2 × radius = 2 × 16 = 32 ft
From the diagram, we can note that:
area of shaded region = area of square - area of circle .............> equation I
1- getting area of square:
Area of a square is the square of its side length
This means that:
Area of square = (32)² = 1024 ft²
2- getting the area of the circle:
Area of circle = πr² = 3.14 × (16)² = 803.84 ft²
3- getting area of shaded region:
Use equation I
area of shaded region = area of square - area of circle
area of shaded region = 1024 - 803.84 = 220.16 ft²
Hope this helps :)
