EASA / CAR Part-66 · Module 1 · 1.3 Geometry · Cat A

Area of a Rectangle, Triangle & Parallelogram

Objective: three shapes, one idea. A triangle is half its enclosing rectangle, and a parallelogram is a rectangle that has been pushed over without losing any area. Drag the shape and watch the area follow the formula.

The shape on a unit grid1 square = 1 m²

Shape

Base b 8 m

Height h 5 m

Lean 0 m

Area

0m²

Base

Height

Grid squares

rectangle A = b × h · triangle A = ½ b h · parallelogram A = b × h

Height means perpendicular height, not the sloping side. This is the single most common mistake in Module 1. The height is measured at right angles to the base, so leaning a parallelogram over changes the length of its sloping sides but not its height, and therefore not its area.

A triangle is exactly half of the rectangle that encloses it. Put a copy of the triangle upside down against the original and the two together make the full rectangle, which is why the formula carries the ½.

Count the squares to check. Each grid square is one square metre, so the area readout should always match the number of squares the shape covers. Use that as a sanity check on any answer in the exam.

Try this: Set the lean to zero, then push it to +5. What happens to the area, and why?
Try this: Make base 8 and height 5 as a rectangle, then switch to a triangle. What fraction of the area is left?
Try this: Find two different base-and-height pairs that give the same area. Is the shape the same?