Question

Find the area of a shaded region in the Fig. where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use $pi=\frac{22}{7}$ and $\sqrt{3}=1.73$)

Answer 1

In equilateral traingle all the angles are of 60°
∴ ∠BAC = 60°
Area of the shaded region = (Area of triangle ABC − Area of sector having central angle 60°) + Area of sector having central angle (360° − 60°)

$=\frac{3\frac{1}{2}}{4}\times A{B}^2-\frac{{60}^0}{360}\times \frac{\pi }{7^2}+\frac{{300}^0}{360}\times \frac{\pi }{7^2}$

$=\frac{3\frac{1}{2}}{4}\times {14}^2-\frac{1}{6}\times \frac{22}{7\times 7^2}+\frac{5}{6}\times \frac{22}{7\times 7^2}$

$=84.77-25.67+128.35$

=187.45 $c{m}^2$
Hence, the area of shaded region is 187.45 \( cm^2\