In a right-angled triangle the hypotenuse is $13$ cm and one of the legs is $5$ cm. Find the area of the triangle.

**Find the other leg.** By Pythagoras: $\text{other leg} = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12$ cm. **Area.** $\dfrac{1}{2} \times 5 \times 12 = 30$ cm². **Why option C (32.5) is tempting.** Picking the *hypotenuse* and the given leg as base × height gives $\tfrac{1}{2} \times 13 \times 5 = 32.5$. But the two perpendicular sides in a right triangle are the *legs*, not the hypotenuse.