Answer:
a) 7 cm
b) 185.5 cm^2
Step-by-step explanation:
a)
Let the side of each of the small square be x.
We have 3 squares that have a side of x.
Then we have a quarter circle with x radius.
The perimeter of the entire figure consists of 6 segments of length x and a quarter circumference of a circle with radius x.
perimeter = 6x + 2(pi)x/4
The perimeter = 53 cm
6x + 2(pi)x/4 = 53
7.571x = 53
x = 7
Answer: The radius is 7 cm.
b)
The area of the whole figure is the area of 3 squares of side 7 cm plus a quarter circle of radius 7 cm.
area = 3s^2 + (pi)r^2/4
area = 3(7 cm)^2 + (pi)(7 cm)^2/4
area = 147 cm^2 + 38.5 cm^2
area = 185.5 cm^2
Answer: The area is 185.5 cm^2
