Question

A rectangular grass lawn is 21m by 10m. In the center, a circular plot of 3.5 m radius is cut for erecting a fountain. Find the area of the grass.

Answer 1

Hint: Subtract the area of the circular plot from the area of the rectangular grass lawn.The area is defined as the space occupied by a flat shape or surface by an object on a two-dimensional plane. The area of a figure is the number of unit square space that it covers, generally expressed in square centimetre or square meter.

Complete step-by-step answer:

The plot for erecting a fountain is a circle which is a round-shaped figure that has no corners or edges; it is also defined as a closed, two-dimensional curved shape whose all points in a plane are at equal distance from a point called the center, whose area is given as\[A = \pi {r^2}\]. The grass lawn is in rectangular shape whose area is given as \[A = l \times b\].
We first evaluate the area of the rectangular lawn and the circular plot, then subtract them to get the area of the grass.
Given the dimension of the rectangular lawn
Length \[l = 21m\]
Breadth \[b = 10m\]
Hence the area of the rectangular grass lawn will be
\[
  {A_1} = l \times b \\
   = 21 \times 10 \\
   = 210{m^2} \\
 \]
Now, the area of the circular plot for erecting a fountain will be where \[r = 3.5m\]
\[
  {A_2} = \pi {r^2} \\
   = \pi {\left( {3.5} \right)^2} \\
   = \dfrac{{22}}{7} \times 3.5 \times 3.5 \\
   = 38.5{m^2} \\
 \]
Hence the area of the grass will be= area of the rectangular grass lawn – the area of circular plot
 \[
  A = {A_1} - {A_2} \\
   = 210 - 38.5 \\
   = 171.5{m^2} \\
 \]
Therefore the area of the grass \[ = 171.5{m^2}\]

Note: To solve this type of question where the area of a specific point is to be found, always subtract the area of the total figure with the area of other regions. Before starting to solve the question, it is always advised to sketch a rough diagram so as to get a clear view.