Question

The area of equilateral triangle is 49 root 3 three arc are drawn wuth the vertice of triangle as cebtre and radius is equal to half of side of triangle find thearea of triangle not included
in sector

Answer 1

GIVEN:

Area of ∆ABC = 49√3

θ = 60° (angle of an equilateral ∆)

Let the each side of the ∆ be a cm.

Area of equilateral triangle = (√3/4) × side ²

49√3 = (√3/4) × a²

a² = 49√3 ×( 4 /√3)  = 49 × 4

a= √49 × 4 = 7 × 2 = 14 cm

Radius of the circle half the length of the side of the ∆ABC (GIVEN)

Radius of the circle = ½ × 14 = 7 cm

Area of sector =(θ/360) × πr²

Area of sector = (60/360) × 22/7 × 7²

= ⅙ × 22 × 7= 154/6 = 77/3 cm²

Required area = Area of ∆ABC - 3 ( area of a sector of angle 60° in a circle of radius 7 cm)

Required area = 49√3 - 3×77/3

= 49√3 - 77

= 49 × 1.73 -77 = 84.77 - 77 = 7.77 cm²

Hence, the area of the  triangle not included in the circle is 7.77 cm²

HOPE THIS WILL HELP