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 :- Side of equilateral ∆ is equal to 1 unit .

To Find :- The area of the incircle is ____ sq. units. ?

Formula used :-

• Inradius of an equaliteral ∆ = (√3/6) * (Side of equaliteral ∆)

Solution :-

Let us assume that, Radius of circle inside given ∆ is equal to r unit .

So,

→ Side of equilateral ∆ = 1 unit .

then, putting value of side in above told formula,

→ r = (√3/6) * 1

→ r = (√3/6) unit .

therefore,

→ Area of incircle = πr²

→ Required area = π * (√3/6) * (√3/6)

→ Required area = π * (3/36)

→ Required area = (π/12) unit² (Ans.)

Hence, The area of the incircle is (π/12) sq. units.

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