Question

Calculate the area of the designed region (shown in the adjoining figure) between the two quadrants of circles of radius 8 cm each.

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Answer 1

Given :

• Radius of circle = 8 cm.
• ∠A = 90°.

To find :

• Calculate the area of the designed region between the two quadrants of circles of radius 8 cm each.

Solution :

The area of shaded region = 2 × Area of segment BD.

To find the area of the shaded region, first we need to find the area of quadrant ABD.

Area of quadrant ABD = $\sf \dfrac {\pi \times r^2}{4} \ = \ \dfrac {1}{4} \times 3.14 \times 8 \times 8$

$\qquad \implies \sf 50.24 \ cm^2$

Area of ∆ABD = $\sf \dfrac {1}{2} \times 8 \times 8$

$\qquad \implies \sf 32 \ cm^2$

Area of segment BD = Area of quadrant ABD - Area of ∆ABD.

Now, we will find the area of segment BD.

$\implies \sf 50.24 \ - \ 32$

$\implies \sf 18.24 \ cm^2$

Area of the shaded region,

$\therefore$ Area of the shaded region = 2 × 18.24

$\implies \sf 36.48 \ cm^2$.

$\therefore$ Area of the shaded region is 36.48 cm².

Answer 2

Area of shaded region = 2 × Area of segment BD

Considering the quadrant ABD...

$area \: of \: quadrant \: abd = \frac{\pi \times {r}^{2} }{4} \\ = \frac{1}{4} \times 3.14 \times 8 \times 8 \\ = 15 .24 {cm}^{2}$

$</p><p>Area \: of \: triangle \: ABD = \frac{1}{2} \times 8 \times 8 \\ = 32 {cm}^{2}$

Therefore,

Area of segment BD = Area of quadrant ABD - Area of triangle ABD

$= 50.24 - 32 \\ = 18.24 \: {cm}^{2}$

Area of shaded region = 2 × 18.24

= 36.48 cm...