Area of 2D Shapes
Grade 4The key area formulas
You need to know these formulas without looking them up:
Rectangle: Area = length × width
Triangle: Area = ½ × base × height
Parallelogram: Area = base × perpendicular height
Trapezium: Area = ½ × (a + b) × h
For the trapezium, a and b are the parallel sides and h is the perpendicular distance between them.
The height must be perpendicular
For triangles and parallelograms, the height must be the perpendicular height — the vertical distance, not the slant side. If the question gives you a slant side, use trigonometry to find the perpendicular height first.
Worked example — trapezium
EXAMPLE
A trapezium has parallel sides of 5 cm and 9 cm, with a perpendicular height of 4 cm. Find its area.
Area = ½ × (5 + 9) × 4 = ½ × 14 × 4 = 28 cm².
Compound shapes
For compound shapes, split them into simpler pieces (rectangles, triangles), find each area separately, then add (or subtract if a piece is cut out).
EXAMPLE
An L-shaped room measures 10 m × 8 m overall with a 4 m × 3 m rectangle cut from one corner. Find the floor area.
Total rectangle area = 10 × 8 = 80 m². Cut-out area = 4 × 3 = 12 m². Floor area = 80 − 12 = 68 m².
