Question

find the perimeter and total area of the composite shape shown below. all measurements are given in inches. use π = 3.14 in any formulas used. perimeter = 65.12 inches, area = 392.96 square inches perimeter = 65.12 inches, area = 292.48 square inches perimeter = 90.24 inches, area = 392.96 square inches perimeter = 12.56 inches, area = 217.12 square inches

Explanation:

Step1: Calculate the perimeter of the semi - circle

The formula for the circumference of a full circle is $C = 2\pi r$. For a semi - circle, the arc length $l=\pi r$. Given $r = 8$ inches, $l = 3.14\times8=25.12$ inches.

Step2: Calculate the perimeter of the rectangular part

The rectangle has two sides of length 12 inches and one side of length 16 inches (the other 16 - inch side is not part of the perimeter of the composite shape). The perimeter contributed by the rectangle is $12 + 12+16 = 40$ inches.

Step3: Calculate the total perimeter

The total perimeter $P$ of the composite shape is the sum of the semi - circle arc length and the perimeter of the rectangular part. So $P=25.12 + 40=65.12$ inches.

Step4: Calculate the area of the semi - circle

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

Step5: Calculate the area of the rectangle

The area of the rectangle $A_{rectangle}=l\times w$, where $l = 16$ inches and $w = 12$ inches. So $A_{rectangle}=16\times12 = 192$ square inches.

Step6: Calculate the total area

The total area $A$ of the composite shape is the sum of the area of the semi - circle and the area of the rectangle. So $A=100.48+192 = 292.48$ square inches.

Answer:

Perimeter = 65.12 inches, Area = 292.48 square inches