If the area of a circle, inscribed in an equilateral triangle is 4\pi cm^2, then what is the area of the triangle?

RRB NTPC Mains or Stage 2 Model Paper 5 with solutions

Question : 10 of 120

Marks: +1, -0

If the area of a circle, inscribed in an equilateral triangle is

4π cm^2,

then what is the area of the triangle?

Solution:

(a) Since, area of circle

= 4π cm^2

(given)

⇒ πr^2 = 4p ⇒ r = 2 cm

In ΔOAD, tan 30º =

{OD}/{AD}⇒ AD

= 2 √3cm

Now, AB

= 2 AD = 4 √3

cm
∴Area of equilateral ΔABC

=√3/4 (AB)^2=√ 3/4 (4√ 3)^2 = 12 √3cm^2

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