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A child makes a poster on a chart paper drawing a square $ A B C D $ of side $ 14 \mathrm{~cm} $. She draws four circles with centre $ A, B, C $ and $ D $ in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles. In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region. (Use $ \pi=22 / 7 $ )"

Academic Mathematics NCERT Class 10

Given:

A child makes a poster on a chart paper drawing a square \( A B C D \) of side \( 14 \mathrm{~cm} \).

She draws four circles with centre \( A, B, C \) and \( D \) in which she suggests different ways to save energy.

The circles are drawn in such a way that each circle touches externally two of the three remaining circles.

To do:

We have to find the perimeter and area of the shaded region.

Solution:

Length of the side of the square $ABCD= 14\ cm$

This implies,

Radius of each of the circle $r= 7\ cm$

Therefore,

Perimeter of the shaded region $=4 \times$ Perimeter of each arc of quadrant

$=4 \times \frac{1}{4}(2 \pi r)$

$=2 \times \frac{22}{7} \times 7$

$=44 \mathrm{~cm}$

Area of the shaded region $=$ Area of the square $-$ Area of four quadrants inside the square

$=(14)^{2}-4 \times \frac{1}{4} \pi 7^{2}$

$=(14)^{2}-\frac{22}{7} \times 7^2$

$=196-154$

$=42 \mathrm{~cm}^{2}$

The perimeter and area of the shaded region are $44\ cm$ and $42\ cm^2$.

Updated on: 10-Oct-2022

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