Question

show that the area of an equilateral triangle is...

Answer 1

As we know that : Every side of equilateral triangle is equal.

Let, the side of an equilateral triangle = x

Then, according to the Pythagoras theoram :

${(Height)}^{2} = {x}^{2} - { (\frac{x}{2} )}^{2} \\ \\ = > Height = \sqrt{ {x}^{2} - \frac{ {x}^{2} }{4} } \\ \\ = > Height = \sqrt{ \frac{3 {x}^{2} }{4} } \\ \\ = > Height = \frac{ \sqrt{3}x }{2}$

Now, as we know that : Area of a triangle

$\frac{1}{2} \times Base \times Height$

So, The Area of an equilateral triangle :

$\frac{1}{2} \times x \times \frac{ \sqrt{3}x }{2} \\ \\ = > \frac{ \sqrt{3} {x}^{2} }{4}$

Then, the area of an equilateral triangle is √3x²/4

HENCE PROVED