Question

If the altitude of an equilateral triangle is 5cm.Then it's area is equal to​

Answer 1

Answer:

Hey mate, Here's your answer ○●□■

Step-by-step explanation:

Pls refer to the attachment ♤♡◇♧

Answer- 625root3/3

Hope it helps u.....○●□■¤☆

Answer 2

The area of an equilateral triangle = $\dfrac{25\sqrt{3}}{3} cm^{2}$

Step-by-step explanation:

Given,

The altitude of an equilateral triangle (h) = 5 cm

Let a be the side of an equilateral triangle.

To find, the area of an equilateral triangle = ?

We know that,

The altitude of an equilateral triangle (h) = $\dfrac{\sqrt{3}}{2} a$

∴ $\dfrac{\sqrt{3}}{2} a$ = 5

⇒ $a=\dfrac{10}{\sqrt{3}} cm$

The area of an equilateral triangle =$\dfrac{\sqrt{3}}{4} a^2$

$=\dfrac{\sqrt{3}}{4} (\dfrac{10}{\sqrt{3}} )^2 cm^{2}$

$=\dfrac{\sqrt{3}}{4} \times\dfrac{100}{3} cm^{2}$

$=\sqrt{3} \times\dfrac{25}{3} cm^{2}$

= $\dfrac{25\sqrt{3}}{3} cm^{2}$

Thus, the area of an equilateral triangle = $\dfrac{25\sqrt{3}}{3} cm^{2}$