Question

In the adjoining figure, PQR
is an equilateral triangle
inscribed in a circle of radius
7 cm. Find the area of the
shaded region.​

Answer 1

Given AB=BC=CA=6 cm

we haveO as the circumcenter

angle OBA=30

in triangle BOM

COS 30=BM/BO

√3/2=3/r

r=2√3cm

Area of shaded region =Area of circle - Area of triangle ABC

Area of shades region =Πr^2-√3/4×side ^2

Area of shaded region =(3.14)×(2√3^2)-√3/4×6^2

Area of shaded region =36.68-15.59

∴ Area of shaded region =22.126 cm sq