CMAT Exam 2023 Shift 2 Solved Paper

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Question : 14 of 100

Marks: +1, -0

What is the area of an equilateral triangle whose inscribed circle has radius

{\R}

?

$4 R^2$
$4 {√{3}} R^2$
$(3+2 {√{2}}) R^2$
$3 {√{3}} R^2$

Solution:

If

{\a}

is the length of equilateral triangle, height is

\;{{√{3}} a}/{2}

\;\text " Inradius "\;=\;{{√{3}} a}/{2} (\;{1}/{3}) =\;{a}/{2 {√{3}}}

It is given,

{\R}=\;{a}/{2 {√{3}}}

Area of triangle

=

Inradius

*

semiperimeter

=R (\;{3 a}/{2}) =\;{3 R}/{2}(2 {√{3}} R)=3 {√{3}} R^2

The answer is option

D

.

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