The area of a trapezium is $176{\text{cm}}^2$, its height is 8 cm and one of its parallel sides is 15 cm. Find the other parallel side.

**Area of a trapezium = ½ × (sum of parallel sides) × height.**

The height is the **perpendicular distance** between the two parallel sides — NOT the slant length of the non-parallel side.

Example: parallel sides 8 cm and 5 cm, height 4 cm. Area = ½ × $(8+5)\times 4$ = ½ × $13\times 4=26{\text{cm}}^2$.

Why ½? You can split a trapezium into a rectangle plus a triangle (or chop and rearrange into a rectangle of the average parallel side). The factor of ½ comes from averaging the two parallel sides.