Question

if the height of the equilateral triangle measures 9cm Find its area

Answer 1

for equilateral triangle=
$height = \frac{ \sqrt{3} }{2} \times base$
$9 = \frac{ \sqrt{3} }{2} base$
$base = \frac{18}{ \sqrt{3} }$
area of triangle=base × height

$= 9 \times \frac{18}{ \sqrt{3} } \\ = \frac{162}{ \sqrt{3} }$

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Answer 2

height of eq triangle=9cm
median of  eq triangle=root3a(where 2a is side of eq tiangle)
root 3a=9
a=9/root 3
a=3root3

area of eq triangle=1/2*base*height=1/2*2a*9=a*9=3root3*9=27root3
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