Find the area of the shaded region in the given figure.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The outer rectangle $ABCD$ has length $L = 26 \, m$ and breadth $B = 12 \, m$.
Area of outer rectangle $= L \times B = 26 \times 12 = 312 \, m^2$.
The inner unshaded region consists of a rectangle and two semi-circles.
The breadth of the inner rectangle is $12 - (4 + 4) = 4 \, m$. This is also the diameter of the two semi-circles.
Radius of each semi-circle $r = 4 / 2 = 2 \, m$.
The length of the inner rectangle is $26 - (3 + 3 + 2 + 2) = 16 \, m$ (subtracting the $3 \, m$ gaps and the two radii of the semi-circles).
Area of inner rectangle $= 16 \times 4 = 64 \, m^2$.
Area of two semi-circles $= 2 \times (\frac{1}{2} \pi r^2) = \pi r^2 = \pi (2)^2 = 4\pi \, m^2$.
Total unshaded area $= 64 + 4\pi \, m^2$.
Area of shaded region $=$ Area of outer rectangle $-$ Total unshaded area
$= 312 - (64 + 4\pi) = (248 - 4\pi) \, m^2$.

Explore More

Similar Questions

$A$ wire fence is to be put up all around a circular ground with diameter $105 \, m$. The length of the fence is $\ldots \ldots \ldots \ldots \, m$.

In a circle with radius $42 \, cm$,an arc subtends an angle of $120^{\circ}$ at the centre. Find the length of this arc and the area of the sector formed by this arc.

If the length of an arc of a circle of radius $r$ is equal to that of an arc of a circle of radius $2r$,then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false? Why?

Difficult
View Solution

In a circle with radius $42 \ cm$,a minor arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor sector and the minor segment corresponding to this arc. (Use $\sqrt{3} = 1.73$)

In a circle,the ratio of the areas of two distinct minor sectors is $1:4$. Then,the ratio of the angles at the centre for those minor sectors is $\ldots \ldots \ldots \ldots$.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo