SSC CPO SI and ASI 2015 Paper

Question : 124 of 199

Marks: +1, -0

A circle is inscribed in an equilateral triangle of side 8 metre. The approximate area of the unoccupied space inside the triangle is

Solution:

(1)

Inradius of an equilateral triangle with side length 8 m is,

{\ { side }}/{2 \√{3}}=\ {8}/{2 \√{3}}= {4 \√{3}}/{3} \ {m}

So, area of the remaining portion (shaded portion) is,

{A}= {\√{3}}/{4}(\ {side})^{2}-\π \ {r}^{2}

⇒ \ {\√{3}}/{4}(8)^{2}-\ {22}/{7} ×(\ {4 \√{3}}/{3}\ ^{2}

=27.7-16.7=11 {m}^{2}

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