Pythagoras' Theorem can be used to calculate the length of the third side of a right angled triangle when given the lengths of the other two sides.

Calculate the area of the following isosceles triangle:

Area of triangle

We know that the base is 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.

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

Area of triangle

Area of triangle