Answer:
The best approximation for the area of the shaded region is 21.5 cm²
Step-by-step explanation:
<em>Area of the shaded region is equal to the area of the square minus the area of the circle</em>
Let us find the area of the square and the area of the circle
- The formula of the area of a square is A = s², where s is its side
- The formula of the area of a circle is A = πr², where r is its radius
∵ The circle touch the 4 sides of the square
∴ The length of the diameter of the circle is equal to the
length of the side of the square
∵ The length of the side of the square = 10 cm
∴ The length of the diameter of the circle = 10 cm
∵ Area of the square = s²
∵ s = 10 cm
∴ Area of the square = (10)²
∴ Area of the square = 100 cm²
∵ The radius of a circle is half its diameter
∵ The diameter of the circle = 10 cm
∴ The radius = × 10 = 5 cm
∴ The area of the circle = πr²
∴ The area of the circle = 3.14(5)²
∴ The area of the circle = 78.5 cm²
Now let us find the shaded area
∵ The shaded area = area of the square - area of the circle
∴ The shaded area = 100 - 78.5
∴ The shaded area = 21.5 cm²
The best approximation for the area of the shaded region is 21.5 cm²