Question

derive the formula for height and area of an equilateral triangle

Answer 1

Using herons formula i have derived the area of equilateral triangle
Hope this will help you
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Answer 2

Area of Equilateral Triangle Formula:  

A = √3/4 a^2

where, “a” denoted the sides of an Equilateral Triangle

Proof:

the sides of an equilateral triangle are equal to “a” units.

We know that the area of Triangle is given by;

A = 1/2×base × height

 

To find the height, consider Triangle ABC,
Applying Pythagoras Theorem we know,

AB^2 = AD^2+BD^2
a^2 = h^2 + (a/2)^2
h^2 = a^2 - (a/4)^2
h^2 = 3a^2/4
h = √3a/2


Thus, we can calculate area by the basic equation,
A = 1/2×b ×h = 1/2×a ×√3a/2

Therefore, A =(√3a)^2/4

hope it helps u:-)