Area of 2D Shapes

Grade 4

The 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.
Nova
Try this one

The diagram shows a composite shape made from a rectangle and a semicircle.

16 cm11 cmsemicircleNot drawn accurately

The rectangle has width \(16\) cm and height \(11\) cm. A semicircle sits on top of the rectangle, with diameter equal to the width of the rectangle.

Work out the total area of the composite shape. Give your answer to 3 significant figures. [3]

Nova's hint:

This question involves finding areas of a rectangle and a semicircle separately, then adding them.

Ask yourself: 'What is the radius of the semicircle if the diameter equals the width of the rectangle?' The area of a semicircle is \( \tfrac{1}{2}\pi r^2 \).

Try to Solve it with Nova?