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 ( = 90.24 ) inches, area ( = 392.96 ) square inches
perimeter ( = 65.12 ) inches, area ( = 292.48 ) square inches
perimeter ( = 12.56 ) inches, area ( = 217.12 ) square inches
perimeter ( = 65.12 ) inches, area ( = 392.96 ) square inches

Explanation:

Step1: Calculate the perimeter of the composite shape

• Perimeter of the semicircle:

The formula for the circumference of a full - circle is \(C = 2\pi r\). For a semicircle, \(C_{semicircle}=\pi r\). Given \(r = 8\) inches and \(\pi=3.14\), \(C_{semicircle}=3.14\times8 = 25.12\) inches.

• Perimeter of the rectangle part (excluding the top side which is covered by the semicircle):

The two vertical sides of the rectangle have length \(12\) inches each, and the bottom side has length \(16\) inches. So the sum of these sides is \(12 + 12+16=40\) inches.

• Total perimeter:

\(P = 25.12+40=65.12\) inches.

Step2: Calculate the area of the composite shape

• Area of the semicircle:

The formula for the area of a full - circle is \(A=\pi r^{2}\). For a semicircle, \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Substituting \(r = 8\) inches and \(\pi = 3.14\), we get \(A_{semicircle}=\frac{1}{2}\times3.14\times8^{2}=\frac{1}{2}\times3.14\times64 = 100.48\) square inches.

• Area of the rectangle:

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 16\) inches and \(w = 12\) inches, so \(A_{rectangle}=16\times12=192\) square inches.

• Total area:

\(A=100.48 + 192=392.96\) square inches.

Answer:

Perimeter = 65.12 inches, Area = 392.96 square inches