Worked example

Calculate the area of the following isosceles triangle:

Diagram of an isoceles triangle with two sides 14.5cm long, and a 12cm base

Answer

Area of triangle  = \frac{1}{2} \times base \times height

We know that the base is 12cm but we do not know the height.

We can find the height by splitting the isosceles triangle into two right-angled triangles and then applying Pythagoras' Theorem to one of them.

Diagram of an isoceles triangle being divided in two.

{h^2} = {14.5^2} - {6^2}

{h^2} = 210.25 - 36

{h^2} = 174.25

h = \sqrt {174.25}

h = 13.20\,(to\,2\,d.p.)

We now know the height of the triangle and can use this to go back and find the area of the isosceles triangle.

Area of triangle  = \frac{1}{2} \times base \times height

Area of triangle  = \frac{1}{2} \times 12 \times 13.20

Area of triangle  = 79.2c{m^2}