Question

a training field is formed by joining a rectangle and two semicircles, as shown below. the rectangle is 98 m long and 62 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 is 98 m and width is 62 m. So, \( A_{rectangle} = 98 \times 62 \).
\( 98\times62 = 6076 \) \( m^2 \)

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

The two semicircles together make a full circle. The diameter of the circle is equal to the width of the rectangle, which is 62 m. So, the radius \( r = \frac{62}{2}= 31 \) m. The area of a circle is \( A_{circle}=\pi r^2 \). Using \( \pi = 3.14 \), we get \( A_{circle}=3.14\times(31)^2 \).
First, calculate \( 31^2 = 961 \). Then, \( 3.14\times961 = 3017.54 \) \( m^2 \)

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. So, \( A_{total}=A_{rectangle}+A_{circle} \).
\( A_{total}=6076 + 3017.54 = 9093.54 \) \( m^2 \)

Answer:

\( 9093.54 \) square meters