Question

what is the perimeter of the figure below? the curves are circular. 25 m
you may round your answer to two decimal places.
diagram of a figure with two semicircular curves and a length of 25 m, and the diameter of the semicircle is 12 m?

Explanation:

Step1: Identify the components of the perimeter

The figure has two straight sides of length 25 m each and two semicircular arcs. The two semicircular arcs together make a full circle. The diameter of each semicircle is 12 m, so the radius \( r = \frac{12}{2}=6 \) m. The circumference of a full circle is \( C = 2\pi r \) or \( C=\pi d \) (where \( d \) is the diameter).

Step2: Calculate the length of the circular part

Using \( C = \pi d \) with \( d = 12 \) m, we get \( C=\pi\times12 = 12\pi \) meters.

Step3: Calculate the length of the straight parts

There are two straight sides, each 25 m, so their total length is \( 2\times25=50 \) meters.

Step4: Calculate the total perimeter

Add the length of the circular part and the length of the straight parts: \( \text{Perimeter}=12\pi + 50 \).

Now, substitute \( \pi\approx3.1416 \):
\( 12\times3.1416 + 50 = 37.6992+50 = 87.6992 \)

Rounding to two decimal places, we get 87.70.

Answer:

87.70 meters