Express the area of an equilateral triangle as a function of the length of a side x.

Solution:

We know that all angles of an equilateral triangle are 60°

In an equilateral triangle, all sides are equal.

Given, length of side = x

Let h be the height of the triangle

Area of an equilateral triangle = (1/2) × base × height

Now, find h using trigonometric ratio,

sin 60° = h/x

h = x sin 60°

h = x (√3/2)

Now, area = (1/2) (x) (√3x/2)

Area = (√3/4)x²

Therefore, the area of the triangle is (√3/4)x² units.

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Express the area of an equilateral triangle as a function of the length of a side x.

Summary:

The area of an equilateral triangle as a function of the length of a side x is (√3/4)x² units.