If the length of the median of an equilateral triangle is x cm, find its area.

Given: Length of the median of the equilateral triangle = x cm

To Find: Area of the equilateral triangle

Concept Used:

Area of an equilateral triangle

Where a = side of the triangle.

Pythagoras theorem: In a right-angled triangle,

(Hypotenuse)² = (Base)² + (Perpendicular)²

Diagram:

Assumption: Let the side of the triangle be x.

Explanation:

∠ADB = 90˚

[Median of an equilateral triangle is a perpendicular bisector]

Applying Pythagoras theorem, in Δ ADB we get,

Now,

Hence, Area of the triangle is .