Question

In Fig. 13.122, two circles of radii 7 cm each are shown. ABCD is a rectangle and AD and BC are the radii. The area of the shaded region is __________.

Answer 1

In the given figure,

BC = CE = DE = 7 cm (Radius of each circle)

Also, the two circles touch each other externally.

We know that if two circles touch each other externally, then the distance between their centres is equal sum of their radii.

CD = CE + ED = 7 + 7 = 14 cm

Now,

Area of the shaded region

= Area of the rectangle ABCD − (Area of quadrant BCEB + Area of quadrant ADEA)

$$\begin{gathered} =\mathrm{CD}\times \mathrm{BC}-\left[\frac{1}{4}\times \mathrm{\pi }{\left(\mathrm{CE}\right)}^2+\frac{1}{4}\times \mathrm{\pi }{\left(\mathrm{DE}\right)}^2\right] \\ =14\times 7-\left[\frac{1}{4}\times \frac{22}{7}\times {\left(7\right)}^2+\frac{1}{4}\times \frac{22}{7}\times {\left(7\right)}^2\right] \\ =98-77 \\ =21{\mathrm{cm}}^2 \end{gathered}$$

In Fig. 13.122, two circles of radii 7 cm each are shown. ABCD is a rectangle and AD and BC are the radii. The area of the shaded region is ___21 cm²___.