Question

find the perimeter of the figure given to the right. use the approximation 3.14 for \\( \pi \\). the perimeter is \\( \square \\) (type a whole number or a decimal rounded to the nearest tenth as needed.) the figure shows a square with side length 22 meters and a semicircle on top with diameter 22 meters.

Explanation:

Step1: Analyze the figure

The figure consists of a square (or rectangle with equal sides) and a semicircle on top. The side length of the square is 22 meters. The diameter of the semicircle is equal to the side length of the square, so \( d = 22 \) meters.

Step2: Calculate the length of the semicircle

The formula for the circumference of a full circle is \( C = \pi d \), so the length of a semicircle is \( \frac{1}{2} \pi d \). Substituting \( d = 22 \) and \( \pi \approx 3.14 \):
\( \frac{1}{2} \times 3.14 \times 22 = 34.54 \) meters.

Step3: Calculate the length of the three sides of the square

The square has four sides, but one side is covered by the semicircle, so we consider three sides. Each side is 22 meters, so the total length for these three sides is \( 3 \times 22 = 66 \) meters.

Step4: Calculate the total perimeter

Add the length of the semicircle and the length of the three sides of the square:
\( 34.54 + 66 = 100.54 \) meters.

Answer:

100.54