Question

Circular arc of radius $7$ cm has been drawn with vertex A of an equilateral triangle ABC of side $14$ cm at center. Find the area of shaded region.

Answer 1

Common area = Area of sector

$=\frac{1}{2}{r}^2\theta =\frac{1}{2}\times 7\times 7\times 60$

$=9\times 30$

$=1470c{m}^2$

Area of circle + Area of eql. $\Delta =$ Area of sector = Area of shaded region

$=\pi r^2+\sqrt{\sqrt{3}}4a^2-1470$

$=\frac{22}{7}\times \times 7+\frac{\sqrt{3}}{4}\times 14\times 14-1470$

$=154+84.77-1470$

$=238.77(\frac{1}{2}\times 7\times 7\times \frac{22}{7\times 3})$ $[\because {60}^{\circ }=\frac{\pi }{3}=\frac{22}{7\times 3}]$

$=238.77-25.66$

$=213.11c{m}^2$