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

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The side of the outer square is $14 \, cm$.
The distance from each side of the square to the inner figure is $3 \, cm$.
The inner figure consists of a central square and four semi-circles attached to its sides.
The side length of the inner square is $14 - (3 + 3) = 8 \, cm$.
Since there are four semi-circles attached to the sides of this $8 \, cm$ square,the diameter of each semi-circle is $8 / 2 = 4 \, cm$,so the radius $r = 2 \, cm$.
Area of the outer square $= 14^2 = 196 \, cm^2$.
Area of the inner square $= 8^2 = 64 \, cm^2$.
Area of the four semi-circles $= 4 \times (\frac{1}{2} \pi r^2) = 2 \pi r^2 = 2 \times \pi \times (2)^2 = 8 \pi \, cm^2$.
Area of the unshaded inner region $= \text{Area of inner square} + \text{Area of four semi-circles} = 64 + 8 \pi \, cm^2$.
Area of the shaded region $= \text{Area of outer square} - \text{Area of unshaded inner region} = 196 - (64 + 8 \pi) = 132 - 8 \pi \, cm^2$.

Explore More

Similar Questions

As shown in the diagram,$\overline{AC}$ is a diameter of the circle with centre $O$. $\Delta ABC$ is inscribed in the circle. If $AC = 35 \, cm$,$AB = 21 \, cm$ and $BC = 28 \, cm$,find the area of the shaded region in $cm^2$.

In the figure,arcs are drawn by taking vertices $A, B$ and $C$ of an equilateral triangle of side $10 \, cm$ as centers to intersect the sides $BC, CA$ and $AB$ at their respective mid-points $D, E$ and $F$. Find the area of the shaded region (Use $\pi = 3.14$) (in $cm^2$).

In $\odot(O, 7),$ the length of $\widehat{ABC}$ is $14.$ Then,$\ldots \ldots$ holds good.

The length of the minute hand of a clock is $10.5 \, cm$. Find the area of the region swept by it between $2.25 \, PM$ and $2.40 \, PM$. (in $cm^2$)

The radii of two concentric circles are $23 \, cm$ and $16 \, cm$. Find the area of the circular ring formed by the circles (in $cm^2$).

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