SSC CHSL 17 Mar 2020 Shift 3 Paper

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Question : 71 of 100

Marks: +1, -0

If the height of an equilateral triangle is

12 {\cm}

, then what is the area of the triangle?

$89.567 {\cm}^{2}$
$96.897 {\cm}^{2}$
$67.9843 {\cm}^{2}$
$83.1384 {\cm}^{2}$

Solution:

Let side of an equilateral triangle be

a

,
Then, height of an equilateral triangle

={\√{3}}/{2} a

∴

{\√{3}}/{2} a=12

[height

=12 {\cm}

, given

]

⇒

a={24}/{\√{3}} {\cm}

Area of equilateral triangle

={\√{3}}/{4} ×{a}^{2}

={\√{3}}/{4} ×{24}/{\√{3}} ×{24}/{\√{3}}

=83.1384 {\cm}^{2}

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