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) x², 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.

AC² = AD² + CD²

(2x)² = (x/2)² + CD²

CD² = (2x)² - (x/2)²

= 4x² - x²/4

= 15 x²/4

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) x²

Therefore, the area function of the isosceles triangle is (√15/4) x², where x is the length of its base.