Question

find the distance around the exterior of the figure below. (assume ( a = 110.00 ) ft and ( b = 60.00 ) ft. round your answer to two decimal places.)

Explanation:

Step1: Analyze the figure's perimeter components

The figure consists of two semi - circles (which together form a full circle) and two straight sides. The formula for the circumference of a circle is \(C = \pi d\), and the diameter \(d=b = 60.00\) ft. The length of the two straight sides is \(2a\), where \(a = 110.00\) ft.

Step2: Calculate the perimeter

The perimeter \(P\) of the figure is the sum of the circumference of the circle and the lengths of the two straight sides.
The circumference of the circle \(C=\pi b\), substituting \(b = 60.00\) ft, we get \(C=\pi\times60\approx3.14159\times60 = 188.4954\) ft.
The sum of the lengths of the two straight sides is \(2a\), substituting \(a = 110.00\) ft, we get \(2\times110=220\) ft.
Then \(P=\pi b+2a\).
Substitute \(a = 110.00\) ft and \(b = 60.00\) ft into the formula:
\(P=3.14159\times60+2\times110\)
\(P = 188.4954+220\)
\(P=408.4954\approx408.50\) ft

Answer:

\(408.50\)