In fig., an equilateral triangle ABC of side 6 cm has been inscribed i

1.	In fig., an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take π = 3.14).
Answer» Given, Side of the equilateral triangle = 6 cm And, The area of the equilateral triangle = √3/4(side)² = √3/4(6)² = √3/4(36) = 9√3 cm² Let us mark the center of the circle as O, OA and OB are the radii of the circle. In triangle BOD, sin 60^o = BD/ OB √3/2 = 3/ OB OB = 2√3 cm = r Therefore, The area of shaded region = Area of the circle – area of the equilateral triangle = πr²– 9√3 = 3.14 x (2√3)² – 9√3 = 3.14 x 12 – 9 x 1.732 = 37.68 – 15.588 = 22.092 cm²

In fig., an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take π = 3.14).

Answer»

Given,

Side of the equilateral triangle = 6 cm

And,

The area of the equilateral triangle = √3/4(side)²

= √3/4(6)²

= √3/4(36)

= 9√3 cm²

Let us mark the center of the circle as O, OA and OB are the radii of the circle.

In triangle BOD,

sin 60^o = BD/ OB

√3/2 = 3/ OB

OB = 2√3 cm = r

Therefore,

The area of shaded region = Area of the circle – area of the equilateral triangle

= πr²– 9√3

= 3.14 x (2√3)² – 9√3

= 3.14 x 12 – 9 x 1.732

= 37.68 – 15.588

= 22.092 cm²