Question

equilateral triangle
The area of an equilateraltri
is 493 cm. Taking each
angular point as centre, a circle
is described with radius equal to
om 00 om
half the length of the side of the
triangle as shown in the figure.
Find the area of the portion in
the triangle not included in the circles​

Answer 1

Answer:

Step-by-step explanation:

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

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