Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

Question

Philoid · Accepted Answer

We know that each interior angle of an equilateral triangle is of measure 60°

Area of sector OCDE = r²

= * * 6 * 6

= cm²

Area of triangle OAB = * (12)²

=

= 36 cm²

Area of circle = πr²

= * 6 * 6

= cm²

Area of shaded region = Area of ΔOAB + Area of circle - Area of sector OCDE

= -

= (36 + ) cm²