Question

a training field is formed by joining a rectangle and two semicircles, as shown below. the rectangle is 91 m long and 68 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 of a rectangle is given by the formula \( A_{rectangle} = length \times width \). Here, length = 91 m and width = 68 m. So, \( A_{rectangle} = 91 \times 68 \).
\( 91\times68 = 6188 \) square meters.

Step2: Calculate area of the two semicircles (which form a circle)

The two semicircles have a diameter equal to the width of the rectangle, so the radius \( r=\frac{68}{2}=34 \) m. The area of a circle is \( A_{circle}=\pi r^{2} \). Using \( \pi = 3.14 \), we get \( A_{circle}=3.14\times(34)^{2} \).
First, calculate \( 34^{2}=1156 \). Then, \( 3.14\times1156 = 3629.84 \) square meters.

Step3: Calculate total area of training field

The total area of the training field is the sum of the area of the rectangle and the area of the circle (formed by two semicircles). So, \( A_{total}=A_{rectangle}+A_{circle} \).
\( A_{total}=6188 + 3629.84=9817.84 \) square meters.

Answer:

\( 9817.84 \) square meters