A circle of radius 2 cm is inscribed in an equilateral triangle. Find the area of the triangle in cm 2.

Question

A circle of radius 2 cm is inscribed in an equilateral triangle. Find the area of the triangle in cm 2. (A) 12 √3 (B) 4 √3 (C) 6 √3 (D) 24 √3

Tardigrade Admin · Accepted Answer

(i) Radius of the circle is one-third of the median of the triangle. (ii) Inradius is 2 cm. (iii) Height of the equilateral triangle =3(2 cm )= 6 cm. (iv) Area of an equilateral triangle =(h2/√3).

Q. A circle of radius $2 c m$ is inscribed in an equilateral triangle. Find the area of the triangle in $c m^{2}$ .

$123$

$43$

$63$

$243$

(i) Radius of the circle is one-third of the median of the triangle.
(ii) Inradius is $2 c m$ .
(iii) Height of the equilateral triangle $= 3 (2 c m) =$ $6 c m$ .
(iv) Area of an equilateral triangle $= \frac{h ^{2}}{3}$ .

Q. A circle of radius 2cm is inscribed in an equilateral triangle. Find the area of the triangle in cm2.

123​

43​

63​

243​