Question

Show that the area of an equilateral triangle is√3/4x^2where x is side of the triangle

Answer 1

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Answer 2

Answer:

Area of equilateral triangle is $\dfrac{\sqrt{3}}{4}x^2$. where x is the side of the triangle.

Step-by-step explanation:

Let an equilateral triangle with the side of x units,

Now,

Draw a perpendicular height from any of the vertex.

The perpendicular will divide the triangle in two equal parts.

So, base = (x/2)

By Pythagoras Theorem,

Length of perpendicular = √[ ( side )^2 - ( side / 2 )^2 ] = √( 4x^2 - x^2 ) / 4

                 = √3x^2 / 4

                 = √3(x/2)

Now,

As we have drawn a perpendicular,

Area of right angled triangle = (1/2)*(√3)(x/2)

                 ⇒ √3/2 x²

Hence, proved.