One isosceles triangle has two sides of 5 cm and a base of 6 cm. A second isosceles triangle has two sides of 5 cm and a base of 8 cm. Which has the greater area?

For the first, the height to the base = √$(5^2-3^2)=4$ cm, so its area = ½ × $6\times 4=12{\text{cm}}^2$. For the second, the height = √$(5^2-4^2)=3$ cm, so its area = ½ × $8\times 3=12{\text{cm}}^2$. The wider base is exactly cancelled by the shorter height — both are $12{\text{cm}}^2$. (Judging by the base alone favours the 8 cm one; 'by $4{\text{cm}}^2$' and 'by $8{\text{cm}}^2$' come from comparing bases or heights instead of products; the 6 cm triangle is not bigger either.)