Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. 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. image of composite shape: a trapezoid with top base 8, bottom base 20, height 8, legs 10 each, and a semicircle on top with radius 4 \\(\bigcirc\\) perimeter = 52.56 inches, area = 162.24 square inches \\(\bigcirc\\) perimeter = 65.12 inches, area = 162.24 square inches \\(\bigcirc\\) perimeter = 46.28 inches, area = 137.12 square inches \\(\bigcirc\\) perimeter = 52.56 inches, area = 137.12 square inches

Explanation:

Step1: Calculate the perimeter

The composite shape consists of a semicircle, two slant sides of the trapezoid, and the bottom base of the trapezoid.

• The diameter of the semicircle is 8 inches, so the radius \( r = \frac{8}{2}=4 \) inches. The length of the semicircular arc is \( \frac{1}{2} \times 2\pi r=\pi r \). Using \( \pi = 3.14 \), this is \( 3.14\times4 = 12.56 \) inches.
• The two slant sides of the trapezoid are each 10 inches, so their total length is \( 10 + 10=20 \) inches.
• The bottom base of the trapezoid is 20 inches.
• Now, sum these lengths: Perimeter \( = 12.56+20 + 20=52.56 \) inches.

Step2: Calculate the area

The composite shape's area is the sum of the area of the semicircle and the area of the trapezoid.

• Area of the semicircle: \( \frac{1}{2}\pi r^{2} \). With \( r = 4 \) and \( \pi = 3.14 \), this is \( \frac{1}{2}\times3.14\times4^{2}=\frac{1}{2}\times3.14\times16 = 25.12 \) square inches.
• Area of the trapezoid: The formula for the area of a trapezoid is \( \frac{(a + b)h}{2} \), where \( a = 8 \), \( b = 20 \), and \( h = 8 \). So, \( \frac{(8 + 20)\times8}{2}=\frac{28\times8}{2}=112 \) square inches.
• Total area: \( 25.12+112 = 137.12 \) square inches.

Answer:

Perimeter \( = 52.56 \) inches, Area \( = 137.12 \) square inches (the last option: Perimeter \( = 52.56 \) inches, Area \( = 137.12 \) square inches)