Question

the area of an equilateral triangle is 100 root 3 cm². taking each vertex as centre of a circle which is described with radius equal to half the length of the side of the triangle .find the area of that part of the triangle which is not included in the circles take pi =3.14 and root 3= 1.732​

Answer 1

Given :-

Area of equilateral triangle = 100√3 cm²

√3/4 a² = 100√3 cm²

a² = 400 cm²

a = √400

a = 20 cm

Therefore, Side of triangle = a = 20 cm

As already mentioned that radius of circle is half of the side of triangle.

r = a/2 = 10 cm

r = 10 cm

Area of 3 sectors = 3(Ø/360° × πr²)

Ar(Sectors) = 180°/360° × 22/7 × 10 × 10

Ar(Sectors) = 1100/7

Ar(Sectors) = 157.14 cm²

Again,

Let Area of triangle not included in in circle = A'

A' = Ar(∆) - Ar(Sectors)

A' = 100√3 - 157.14

A' = 173.2 - 157.14 cm²

A' = 16.06 cm² Answer.....

Answer 2

Refer to attachment

hope it helps