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 ( = 28.84 ) inches, area ( = 54.39 ) square inches
perimeter ( = 14.71 ) inches, area ( = 26.13 ) square inches
perimeter ( = 19.42 ) inches, area ( = 54.39 ) square inches
perimeter ( = 19.42 ) inches, area ( = 26.13 ) square inches

Explanation:

Step1: Calculate the perimeter

• The perimeter of the composite shape is the sum of the arc length of the semicircle and the two sides of the triangle.
• The formula for the arc length of a semicircle is \(l=\pi r\) (where \(r = 3\) inches). So, \(l=3.14\times3=9.42\) inches.
• The two sides of the triangle are each \(5\) inches.
• Perimeter \(P=9.42 + 5+5=19.42\) inches.

Step2: Calculate the area

• The area of the composite shape is the sum of the area of the semicircle and the area of the triangle.
• The formula for the area of a semicircle is \(A_{semicircle}=\frac{1}{2}\pi r^{2}\) (where \(r = 3\) inches). So, \(A_{semicircle}=\frac{1}{2}\times3.14\times3^{2}=\frac{1}{2}\times3.14\times9 = 14.13\) square inches.
• The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}bh\) (where \(b=6\) inches and \(h = 4\) inches). So, \(A_{triangle}=\frac{1}{2}\times6\times4=12\) square inches.
• Total area \(A=14.13+12 = 26.13\) square inches.

Answer:

Perimeter \( = 19.42\) inches, Area \( = 26.13\) square inches (the fourth option).