Question

A
The area of an equila
is 49 3 cm. Takin
angular point as centre
of an equilateral triangle
3 cm. Taking each
hat point as centre, a circle
is described with radius equal to
me length of the side of the
triangle as shown in the figure.
7 cm
7 cm
7 cm
7 cm
600
2 600
7 cm
1 cm
ud the area of the portion in
the triangle not included in the
circles.
Four equal circles, each of rad
ual circles, each of radius 'a' touch one another. Find the area between​

Answer 1

Answer:

Step-by-step explanation:

★ Brainly Teacher ★

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

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