Worked example
Calculate the area of the following isosceles triangle:
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.
\({h^2} = {14.5^2} - {6^2}\)
\({h^2} = 210.25 - 36\)
\({h^2} = 174.25\)
\(h = \sqrt {174.25}\)
\(h = 13.20\,(to\,2\,d.p.)\)
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 \( = 79.2c{m^2}\)