Question

a training field is formed by joining a rectangle and two semi - circles, as shown below. the rectangle is 83 m long and 60 m wide. find the area of the training field. use the value 3.14 for π, and do not round your answer. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of rectangle

The area formula for a rectangle is $A = l\times w$, where $l = 83$ m and $w=60$ m. So, $A_{rectangle}=83\times60 = 4980$ m².

Step2: Calculate area of two - semi - circles (which is equivalent to one full - circle)

The two semi - circles together form a circle. The diameter of the circle is equal to the width of the rectangle, so $d = 60$ m, and the radius $r=\frac{d}{2}=\frac{60}{2}=30$ m. The area formula for a circle is $A=\pi r^{2}$. Using $\pi = 3.14$ and $r = 30$ m, we have $A_{circle}=3.14\times30^{2}=3.14\times900 = 2826$ m².

Step3: Calculate total area of the training field

The total area of the training field $A_{total}=A_{rectangle}+A_{circle}$. So, $A_{total}=4980 + 2826=7806$ m².

Answer:

$7806$ m²