A pentagonal field splits into a trapezium of area $138{\text{m}}^2$ and a triangle whose base is 16 m and height is 9 m. Grass seed is spread over the whole field at ₹15 per square metre. Find the total cost.

**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.