Question

In the given figure, the triangle is equilateral in nature and has a side equal to 1 unit.
The area of the incircle is ____ sq. units.

Answer 1

Given : the triangle is equilateral

has a side equal to 1 unit.

To Find : The area of the incircle

Solution:

Area of an Equilateral Triangle = (√3  / 4) side²

= (√3 / 4) 1²

= √3 / 4

Area of a triangle = rs

s = semi perimeter of triangle

r = radius of incircle

s = ( 1 + 1 + 1)/2  = 3/2

Hence Area of triangle  = 3r/2

3r/2 = √3 / 4

=>    1/2√3

Area of circle   = πr²

The area of the incircle is   π (1/2√3)²

= π/12  sq units

= 0.262 sq units

Learn More:

In a triangle abc the incircle touches the sides bc,ca and ab ...

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then circumcentre of triangle is

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