Question

find the distance around the exterior of the figure below. (assume d = 20.0 cm. round your answer to one decimal place.)

Explanation:

Step1: Calculate the circumference of the semicircle

The formula for the circumference of a full - circle is \(C = \pi d\). For a semicircle, the length of the curved part is \(l=\frac{1}{2}\pi d\). Given \(d = 20.0\) cm, then \(l=\frac{1}{2}\times\pi\times20.0= 10\pi\) cm.

Step2: Calculate the total perimeter of the figure

The figure has a straight side of length \(d\) (since the diameter is part of the perimeter). The total perimeter \(P\) of the figure is the sum of the length of the curved part and the diameter. So \(P=\frac{1}{2}\pi d + d\). Substitute \(d = 20.0\) cm: \(P=10\pi+20\). Using \(\pi\approx3.14\), we get \(P = 10\times3.14+20=31.4 + 20=51.4\) cm.

Answer:

\(51.4\)