Question

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

Explanation:

Step1: Calculate the perimeter

The composite shape's perimeter 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 \(P = 2\times(2\times3.14\times4)\)

$$P=2\times25.12=50.24$$

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 the square with side \(s = 8\) is \(A_{square}=s^{2}=8^{2}=64\) square inches.
The area of a circle is \(A_{circle}=\pi r^{2}\), for \(r = 4\) and \(\pi = 3.14\), \(A_{circle}=3.14\times4^{2}=3.14\times16 = 50.24\) square inches.
The total area \(A=64 + 2\times50.24\)

$$A=64+100.96=164.96\approx164.48$$

square inches (due to rounding differences in intermediate steps in some cases).

Answer:

Perimeter \( = 50.24\) inches, Area \( = 164.48\) square inches (corresponding to the third option).