Question

Show that the area of a equilateral triangle is root 3 divided by 4 multiply by
x square where X is side of a triangle

Answer 1

Let x be the side of an equilateral ∆ABC.

From vertex A draw a perpendicular to BC.

Let the point be D.

Let the perpendicular be h.

A new right angled triangle will be formed ∆ADC.

By Pythagoras' Theorem,

AC^2 = AD^2+DC^2

side^2= h^2 + (s/2)^2

x^2 - s^2/4=h^2

h^2 = 3x^2/4...... making denominators same for subtraction

h = 3x/4...... taking square roots

Area of a triangle = 1/2 × b × h

= 1/2 × x × 3x/4 ....... solving it further we get area of an equilateral ∆ = √3/4 × x.