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 \\( = 12.56 \\) inches, area \\( = 114.24 \\) square inches perimeter \\( = 100.48 \\) inches, area \\( = 164.48 \\) square inches perimeter \\( = 50.24 \\) inches, area \\( = 164.48 \\) square inches

Explanation:

Step1: Calculate the perimeter

The composite shape's perimeter is composed of 4 semi - circles (which is equivalent to 2 full circles). The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r = 4\) inches and \(\pi=3.14\).

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Step2: Calculate the area

The area of the composite shape is the sum of the area of the square (\(A_{square}=s^{2}\), where \(s = 8\) inches) and the area of 2 full circles (\(A_{circle}=\pi r^{2}\), \(r = 4\) inches).

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Answer:

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