Answer:
Area = 5π/2 in^2
Perimeter = 3π + 2 in
Explanation:
A=area of a circle. P=Perimeter of a circle
F=Area of first semi-circle
T=Area of Figure
Solve for Area:
A=πr^2
F=A/2
A=π(2)^2 ==> solve for A
A=4π
F=(4π)/2
F=2π ==> this is for the first semi-circle
S=Area of second semi-circle
S=(πr^2)/2
S=(π(2/2)^2)/2 ==> the radius is half the diameter, and the diameter is 2 in
S=(π(1)^2)/2
S=π/2
T=F+S ==> The total area is the area of both semi-circles
T=2π + π/2 ==> plugin 2π for F and π/2 for S
T = 4π/2 + π/2 ==> common denominators
T = 5π/2 in^2
Now solve for perimeter
P = 2πr.
q = perimeter of first semi-circle
q = P/2
q = 2πr/2
q = 2π(2)/2 ==> plugin 2 for r
q = 2π
R = Perimeter of second semi-circle
R = 2π(1)/2 ==> we calculated that the radius of the semi-circle is half of the
radius of the first semi-circle
R = 2π/2 ==> simplify
R = π
Also, add in side length DC into the perimeter as it is part of the perimeter.
E = Entire perimeter of figure
E = q + R + DC
E = 2π + π + 2
E = 3π + 2 in