Question

a landscaper is designing a semicircular flower bed with a diameter of 6 meters. what is the perimeter of the flower bed, including the straight edge?
a. 15.42 meters
b. 9.42 meters
c. 18.84 meters
d. 24.84 meters

Explanation:

Step1: Find the circumference of the full - circle

The formula for the circumference of a circle is \(C = \pi d\). Given \(d = 6\) meters and \(\pi\approx3.14\), then \(C=\pi\times6 = 18.84\) meters.

Step2: Find the length of the semicircular arc

The length of the semicircular arc \(l=\frac{C}{2}\). Since \(C = 18.84\) meters, \(l=\frac{18.84}{2}=9.42\) meters.

Step3: Calculate the perimeter of the semicircular flower - bed

The perimeter \(P\) of the semicircular flower - bed (including the straight edge) is the sum of the length of the semicircular arc and the diameter. So \(P=l + d\). Substitute \(l = 9.42\) meters and \(d = 6\) meters, we get \(P=9.42+6=15.42\) meters.

Answer:

A. 15.42 meters