Question

if the given altitude of an equilateral triangle is root 6 cm find the area. ​

Answer 1

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Given:

i)Equilateral triangle

ii)Height(h) is √6 cm

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To find:

Area

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Answer:

First, we have to find the length of side of the equilateral triangle:-

• Consider the right angled triangle ADC in the above image

AD=h=√6

DC=a/2

AC=a

Apply Pythagoras Theorem,

(√6)²+(a/2)²=(a²)

=>6+(a²/4)=a²

=>6=(a²)-(a²/4)

=>24=3a²

=>a=√8 cm

Now apply the formula for the area of an equilateral triangle:-

$area = \frac{ \sqrt{3} }{4} {a}^{2}$

where, a is the side(and not the height, so do not confuse it with height)

$area = \frac{ \sqrt{3} }{4} ( { \sqrt{8} })^{2}$

$area = 2 \sqrt{3}$

Ans. =2√3cm²