# The base of an isosceles triangle is half as long as the two equal sides. What is the area function of this triangle?

An isosceles triangle is a triangle with two equal sides.

### Answer: Area function of isosceles triangle = (√15/4) x^{2}, where x is the length of its base.

We will let the length of the base of an isosceles triangle be x. Then, the other two equal sides are 2x.

**Explanation:**

Consider the isosceles triangle ABC shown below with equal sides AC and BC.

Let us apply Pythagoras Theorem in Triangle ACD.

AC^{2} = AD^{2} + CD^{2}

(2x)^{2} = (x/2)^{2} + CD^{2}

CD^{2} = (2x)^{2} - (x/2)^{2}

= 4x^{2} - x^{2}/4

= 15 x^{2}/4

CD = (√15/2) x

The area of a triangle is given by the formula 1/2 × Base × Height.

Area of Isosceles Triangle = 1/2 × x × (√15/2) x = (√15/4) x^{2}