Question

Show that the area of an equilateral triangle is root 3 by 4 x square

Answer 1

Step 1: Since all the 3 sides of the triangle are same,

AB = BC = CA = a

Step 2: Find the altitude of the △ABC.

Draw a perpendicular from point A to base BC, AD ⊥ BC

By using Pythagoras theorem

In △ ADC

h2 = AC2 - DC2

= a2 - (a2)2 [Because, DC = a2 ]

= a2 - a24

h = √3a2

Step 3: We know that, Area of a triangle = 12

* Base * Height

= 12 * a * √3a2

= √3/4a2

The area of a equilateral triangle = √3/4a2.