Area of a Trapezium

A trapezium has at least one pair of parallel sides, and its area is the average of those two sides times the perpendicular height: \(A = \frac{1}{2}(a + b)h\). This NSW Year 8 maths subtopic (NESA outcome MA4‑ARE‑C‑01) shows why, by fitting two copies together to make a parallelogram.

You will spot the parallel sides when a trapezium leans or lies on its side, find areas with mixed units, and work backwards to a height or a missing parallel side. You will also tile the wall of a swimming pool, buy boxes of lawn seed, give a block of farmland in hectares and find the glass in a window made of a rectangle and a trapezium. It is part of Year 8 Area and Perimeter.