Question

Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made. [Use `sqrt(3) = 1.73` and π = 3.14.]

Answer 1

In equilateral traingle all the angles are of 60°

∴ ∠ABO = ∠AOB = 60°

Area of the shaded region = (Area of tringle AOB - Area of sector having central angle 60°) +Area of sector having central angle (360° - 60°)

`= sqrt(3)/4("AB")^2 - 60^circ/360^circ pi (6)^2+(300°)/(360°)pi(6)^2`

`=1.73/4(12)^2-1/6xx3.14xx(6)^2+5/6xx3.14(6)^2`

=62.28-18.84 + 94.2

= 137.64 cm²

Hence, the area of shaded region is 137.64 cm²