Question

one side of an equilatral triangle is 30cm. its area is:

Answer 1

we know that area of equilateral ∆ is √3/4 a²
a = 30cm
=> area = 30×30√3/4
= 225 √3 cm²

Answer 2

We know that the an equilateral triangle is a special kind of triangle in which all the three sides are equal as well as in this kind of triangle each angle measures 60 degrees.

A special formula exists to find the area of an equilateral triangle which is mentioned below:

$\bold{\frac{\sqrt{3} }{4} \times (side)^{2}}$ , where side refers to the each equal side of the equilateral triangle.

We are given the measure of each side of the triangle.

Side of equilateral triangle = 30 cm

Substituting the value of each side in the formula,

$\bold{\frac{\sqrt{3}} {4} \times ( 30 )^2~cm^2}$

$\bold{\frac{\sqrt{3} }{4} \times 900~cm^2}\\ \\ \bold{\frac{900\sqrt{3} }{4}~cm^2 }\\ \\ \bold{225 \sqrt{3}~cm^2}\\ \\ \bold{389.711431703~cm^2}$

On rounding off,

Area of the equilateral triangle = 389.71 cm^2