In triangle ABC the angle at B is a right angle, AB = 20 cm and BC = 21 cm. What is the area of the triangle?

The two sides that enclose the right angle are the base and the height, so no extra work is needed: area = ½ × $20\times 21=210{\text{cm}}^2$. (The hypotenuse is AC = √(400 + 441) = √841 = 29 cm, but it plays no part here — using it as a base without its own altitude would wrongly give $290{\text{cm}}^2$.) Forgetting the factor ½ gives $420{\text{cm}}^2$.