Question

find the area of equilateral triangle whose altitude is 16 under root 3 cm

Answer 1

let side =2x
x^2 +16root3^2=(2x)^2
256×3=4x^2-x^2
768=3x^2
768/3=x^2
256=x^2
x=16
side =32

Answer 2

The area of equilateral triangle is "$256\sqrt{3}cm^{2}$".

Step-by-step explanation:

We have,

The altitude of equilateral triangle = 16$\sqrt{3}$ cm

To find, the area of equilateral triangle = ?

Let the side of equilateral triangle = a

We know that,

The altitude of equilateral triangle $=\dfrac{\sqrt{3}}{2} a$

∴ $\dfrac{\sqrt{3}}{2} a= 16\sqrt{3}$

⇒ $a=16\times 2=32cm$

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

$=\dfrac{\sqrt{3}}{4} (32)^{2}$

$=\dfrac{\sqrt{3}}{4} 32\times 32$

$=\sqrt{3} \times 8\times 32 cm^{2}$

$=256\sqrt{3}cm^{2}$

Hence, the area of equilateral triangle is $256\sqrt{3}cm^{2}$.