Question

a playing field is made up of a rectangle of length 100 m and breadth 40 m, and 2 semicircles at the respective ends. what is the total area rounded to 1 decimal place? use π = 3.142

Explanation:

Step1: Calculate area of rectangle

The area of a rectangle is given by the formula \( A_{rectangle} = length \times breadth \). Here, length is 100 m and breadth is 40 m. So, \( A_{rectangle}=100\times40 = 4000 \, m^2 \).

Step2: Calculate area of two semicircles

Two semicircles make a full circle. The diameter of the circle is equal to the breadth of the rectangle, which is 40 m. So, the radius \( r=\frac{40}{2}=20 \, m \). The area of a circle is \( A_{circle}=\pi r^2 \). Using \( \pi = 3.142 \), we get \( A_{circle}=3.142\times(20)^2=3.142\times400 = 1256.8 \, m^2 \).

Step3: Calculate total area

The total area of the playing field is the sum of the area of the rectangle and the area of the circle. So, \( A_{total}=A_{rectangle}+A_{circle}=4000 + 1256.8=5256.8 \, m^2 \).

Answer:

5256.8