Question

If the altitude of a equilateral triangle is √5 cm then find its area.

Answer 1

This is the answer. Hope this will help you.

Answer 2

The area of the equilateral triangle is $\frac{5}{\sqrt{3}}\ cm^2$.

Step-by-step explanation:

Given : If the altitude of a equilateral triangle is $\sqrt{5}$ cm.

To find : Its area ?

Solution :

The altitude of the equilateral triangle is

$h=\frac{\sqrt{3}}{2}a$

Substitute $h=\sqrt{5}$,

$\sqrt{5}=\frac{\sqrt{3}}{2}a$

$a=\frac{2\sqrt{5}}{\sqrt3}$

The area of the equilateral triangle is

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

Substitute the value,

$A=\frac{\sqrt{3}}{4}(\frac{2\sqrt{5}}{\sqrt3})^2$

$A=\frac{\sqrt{3}}{4}\times\frac{20}{3}$

$A=\frac{5}{\sqrt{3}}\ cm^2$

Therefore, the area of the equilateral triangle is $\frac{5}{\sqrt{3}}\ cm^2$.

#Learn more

If the altitude of an equilateral triangle is 5cm, then it's area equal to

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