The area of the incircle of an equilateral triangle of side 42 cm isa 223 cm 2b 231 cm 2c 462 cm 2d 924 cm 2

Let ABC be the equilateral triangle such that AB = BC = CA = 42 cm. Also, let O be the centre and nbsp;r nbsp;be the radius of its nbsp;incircle. AB, B ...

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Byju's Answer

Standard X

Mathematics

Lengths of Tangents Drawn from External Point

The area of t...

Question

The area of the incircle of an equilateral triangle of side 42 cm is

(a) $22 \sqrt{3} c m^{2}$

(b) 231 cm²

(c) 462 cm²

(d) 924 cm²

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Solution

Let ABC be the equilateral triangle such that AB = BC = CA = 42 cm. Also, let O be the centre and r be the radius of its incircle.

AB, BC and CA are tangents to the circle at M, N and P.

∴ OM = ON = OP = r

Area of ΔABC = Area (ΔOAB) + Area (ΔOBC) + Area (ΔOCA)

Area of the circle =

Hence, the correct answer is option (c).

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The area of the incircle of an equilateral triangle of side 42 cm is (a) 223 cm2 (b) 231 cm2 (c) 462 cm2 (d) 924 cm2

The area of the incircle of an equilateral triangle of side 42 cm is

(a) $22 \sqrt{3} c m^{2}$

(b) 231 cm²

(c) 462 cm²

(d) 924 cm²