17.5% of the area inside the square is shaded.
To solve this problem
W can find the side length of the square using the formula for the perimeter of a square:
Perimeter = 4s
Where
s is the side length of the square.
In this case, we have:
40 cm = 4s
Dividing both sides by 4, we get:
s = 10 cm
We can use the formula for the area of a square to get the square's area since we know its side length:
Area = s²
In this case, we have:
Area = 10 cm²
The area of the shaded area needs to be determined now. The area that is shaded has a 7 cm diameter, forming a semicircle. The following formula determines a circle's area:
Area = πr²
Where
r is the radius of the circle. In this case, we have:
Area = π(7 cm/2)²
Dividing both sides by 2, we get:
Area = 7π cm²
Since the shaded region is a semicircle, its area is half the area of the full circle, or 7π cm² / 2.
We must divide the area of the darkened zone by the square's area and multiply the result by 100% to determine the percentage of the square that is shaded:
Shaded area percentage = (7π cm² / 2) / (10 cm²) * 100%
Simplifying, we get:
Shaded area percentage = 17.5%
So, 17.5% of the area inside the square is shaded.
Here is the complete option :