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

Nine circular designs are made in a square show-piece as shown in the diagram. If the radius of each circle is $21\, cm$,find the area of the region without design. (in $cm^2$)

$A$ cow is tied with a rope of length $14 \, m$ at the corner of a rectangular field of dimensions $20 \, m \times 16 \, m$. Find the area of the field in which the cow can graze. (in $m^2$)

Find the area of the sector of a circle of radius $5\, cm$,if the corresponding arc length is $3.5\, cm$. (in $cm^2$)

If the perimeter of a circle is equal to that of a square,then the ratio of their areas is

In $\odot(O, 5.6)$,$\overline{OA}$ and $\overline{OB}$ are radii perpendicular to each other. Then,the difference between the area of the minor sector formed by minor $\widehat{AB}$ and the corresponding minor segment is $\ldots \ldots \ldots \ldots cm^2$.

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