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.
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