Question

If the side of an equilateral triangle is ‘a’ unit, prove that its area is √3/4 ×a2.​

Answer 1

Step-by-step explanation:

Suppose ABC is an equilateral triangle having AB =BC = CA = a. 

Suppose AD is the altitude drawn from the vertex A to the side BC. 

So, It will bisects the side BC:. DC = 1/2a

Now, In right triangle ADC

By using Pythagoras theorem,

we have AC² = CD² + DA²

⇒a² - (-1/2a)² + DA²

⇒ DA² = a² - 1/4a²

⇒ DA² = 3/4a²

⇒ DA =

$\frac{ \sqrt{3} }{2} a {}^{2}$

Now, area (triangle ABC) =1/2×BC×AD

=1/2×a×√3/2a

=√3/4×a²