Area of a trapezium

Average the parallel sides, then multiply by the height.

Key formulas

Only the parallel pair a and b enter the average. The non-parallel sides (legs) are not averaged.

Parallel sides 7 and 13, height 5 → area = ½(20)×5 = 50.

If height is missing, drop perpendiculars from the ends of the shorter base to split a rectangle and right triangles.

Problem. A trapezium has parallel sides 7 cm and 13 cm and height 5 cm. Find its area.

Solution. Area = ½(a+b)h = ½(7+13)×5 = 50 cm².

Height must be perpendicular distance between the parallel sides.

Parallels 9 and 15, height 4. Area is:

Legs equal and base angles equal; area formula unchanged.