Answer:
Answer: (Second choice)
Perimeter= 50.24 inches, Area=164.48 square inches
Step-by-step explanation:
Compound Shapes
The figure in the image can be split into four half circles and a square.
The area of a circle of radius r is:
[tex]A_c=\pi r^2[/tex]
The area of a square of side length x is:
[tex]A_s=x^2[/tex]
Each semicircle has a radius of r=4 inches, thus the area of the four semicircles is twice the area of a circle:
[tex]A_1=2\pi\cdot 4^2[/tex]
[tex]A_1=2*3.14* 16 =100.48\ in^2[/tex]
The square has a side length of x=8 inches:
[tex]A_2=8^2=64 \ in^2[/tex]
The total area of the shape is
[tex]A=A_1+A_2=100.48+64=164.48\ in^2[/tex]
The perimeter of the figure corresponds to the length of 4 semicircles or twice the length of a circle:
[tex]P=2*(2\pi r)=2*2*3.14*4=50.24\ in[/tex]
Answer: (Second choice)
Perimeter= 50.24 inches, Area=164.48 square inches
