"
">

A plot is in the form of a rectangle $ A B C D $ having semi-circle on $ B C $ as shown in figure below. If $ A B=60 \mathrm{~m} $ and $ B C=28 \mathrm{~m} $, find the area of the plot.
"

Academic Mathematics NCERT Class 10

Given:

A plot is in the form of a rectangle \( A B C D \) having semi-circle on \( B C \).

\( A B=60 \mathrm{~m} \) and \( B C=28 \mathrm{~m} \)

To do:

We have to find the area of the plot.

Solution:

The given plot is formed by a rectangle $ABCD$ and one semicircle on $BC$ as diameter.

Length of the rectangle $AB (l) = 60\ m$
Breadth of the rectangle $BC (b) = 28\ m$

This implies,

Radius of semicircle $(r) = \frac{1}{2}(BC)$

$=\frac{1}{2}(28)$

$= 14\ m$

Therefore,

Area of plot $=$ Area of rectangle ABCD $+$ Area of semicircle

$=l \times b+\frac{1}{2} \pi r^{2}$

$=60 \times 28+\frac{1}{2} \times \frac{22}{7}(14)^{2} \mathrm{~m}^{2}$

$=1680+\frac{22}{14} \times 14 \times 14 \mathrm{~m}^{2}$

$=1680+308 \mathrm{~m}^{2}$

$=1988 \mathrm{~m}^{2}$

The area of the plot is $1988 \mathrm{~m}^{2}$.

Updated on: 10-Oct-2022

33 Views

Kickstart Your Career

Get certified by completing the course

Advertisements