Question

topic: circles
progress
question id: 1192382
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.
12
16
perimeter = 90.24 inches, area = 392.96 square inches
perimeter = 65.12 inches, area = 392.96 square inches
perimeter = 65.12 inches, area = 292.48 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 rectangle 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). So the sum of the relevant sides of the rectangle is $12 + 12+16=40$ inches.

Step3: Calculate the total perimeter

The perimeter $P$ of the composite shape is the sum of the semi - circle arc length and the relevant rectangle sides, $P=25.12 + 40=65.12$ 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 $A_{rectangle}=12\times16 = 192$ square inches.

Step6: Calculate the total area

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

Answer:

Perimeter = 65.12 inches, Area = 292.48 square inches