Question

find the perimeter and total area of the composite shape shown below. all measurements are given in inches. use ( pi = 3.14 ) in any formulas used. perimeter ( = 50.24 ) inches, area ( = 264.96 ) square inches perimeter ( = 50.24 ) inches, area ( = 164.48 ) square inches perimeter ( = 100.48 ) inches, area ( = 164.48 ) square inches perimeter ( = 12.56 ) inches, area ( = 114.24 ) square inches

Explanation:

Step1: Calculate the perimeter

The perimeter of the composite shape is composed of 4 semi - circles with radius \(r = 4\) inches. The 4 semi - circles are equivalent to 2 full circles.
The formula for the circumference of a circle is \(C=2\pi r\).
For \(r = 4\) and \(\pi=3.14\), the perimeter \(P = 2\times(2\pi r)=4\pi r\).
Substitute \(r = 4\) into the formula: \(P=4\times3.14\times4=50.24\) inches.

Step2: Calculate the area

The area of the composite shape is the sum of the area of the square and the area of 2 circles.
The area of a square with side length \(s = 8\) is \(A_{square}=s^{2}=8^{2}=64\) square inches.
The formula for the area of a circle is \(A=\pi r^{2}\). For \(r = 4\) and \(\pi = 3.14\), the area of one circle is \(A_{circle}=\pi r^{2}=3.14\times4^{2}=3.14\times16 = 50.24\) square inches.
The area of 2 circles is \(A_{circles}=2\times50.24 = 100.48\) square inches.
The total area \(A=A_{square}+A_{circles}=64 + 100.48=164.48\) square inches.

Answer:

Perimeter \( = 50.24\) inches, Area \( = 164.48\) square inches (the second option).