Question

The area of an equilateral triangle is 49√3 cm².Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circle.( Take √3 = 1.73).

Answer 1

FIGURE IS IN THE ATTACHMENT

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 YOU...

Answer 2

Answer :- Area of the triangle is 7.77 square cm.