Question

Find the area of equilateral triangle whose altitude is 16v3 cm.​

Answer 1

The area of equilateral triangle is "144· $\sqrt{3}$   $cm^{2}$".

Step-by-step explanation:

Let  side of an equilateral triangle = a

Given, altitude (h) = 16 × $\sqrt{3}$ cm

∴ Altitude of equilateral triangle = $\dfrac{\sqrt{3}}{2}$ × side(a)

= $\dfrac{\sqrt{3}}{2}$ × 16$\sqrt{3}$ cm

= 24 cm

We know that,

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

The area of equilateral triangle = $\dfrac{\sqrt{3}}{4}$ × $24^{2}$ $cm^{2}$

= $\sqrt{3}$  × 24 × 6 $cm^{2}$

= 144· $\sqrt{3}$   $cm^{2}$

Hence,  the area of equilateral triangle is "144· $\sqrt{3}$   $cm^{2}$".