Question

hotspot label
question 3
listen
using the image of the track, find and label the areas of the rectangle and the two semicircles that make up the grassy area inside the track.
all units are in meters squared. use 3.14 as an approximation for π. do not round your answer.
hotspot 2
area of a rectangle = length * width
hotspots 1 and 3
radius = diameter ÷ 2
area of a semicircle = \\( \frac{\pi r^{2}}{2} \\)
press each hotspot and type your answer.
a running track

Explanation:

Step1: Calculate the width of the rectangle

The diameter of the semicircle is \(73m\), which is the width of the rectangle.

Step2: Calculate the area of the rectangle

Using the formula \(A = length\times width\), with \(length = 84.39m\) and \(width = 73m\).
\(A_{rectangle}=84.39\times73 = 6160.47m^{2}\)

Step3: Calculate the radius of the semicircle

Using the formula \(r=\frac{d}{2}\), with \(d = 73m\).
\(r=\frac{73}{2}=36.5m\)

Step4: Calculate the area of one - semicircle

Using the formula \(A_{semicircle}=\frac{\pi r^{2}}{2}\), with \(\pi = 3.14\) and \(r = 36.5m\).
\(A_{semicircle}=\frac{3.14\times(36.5)^{2}}{2}=\frac{3.14\times1332.25}{2}=2090.185m^{2}\)

Step5: Calculate the area of two semicircles

Since two semicircles make a full circle, \(A_{two - semicircles}=\pi r^{2}\) (or \(2\times\frac{\pi r^{2}}{2}\)).
\(A_{two - semicircles}=3.14\times(36.5)^{2}=3.14\times1332.25 = 4180.37m^{2}\)

Answer:

The area of the rectangle is \(6160.47m^{2}\) and the area of the two semicircles is \(4180.37m^{2}\)