These questions ask you to calculate a covered surface, recover a missing base or height, and distinguish the formulas for rectangles, parallelograms and triangles. Identify the shape and the perpendicular measurements before using any numbers.
Match each shape to its area rule
| Shape | Rule and tiny example |
|---|---|
| Rectangle | Multiply length by width. A rectangle 7 cm by 3 cm has area 7 times 3, which is 21 cm². |
| Rectangle with four equal sides | Multiply the side by itself. A side of 5 cm gives 5 times 5, which is 25 cm². |
| Parallelogram | Multiply the base by the perpendicular height. A base of 11 cm and height of 3 cm give 33 cm². |
| Triangle | Take half of base times perpendicular height. A base of 9 cm and height of 4 cm give half of 36, which is 18 cm². |
Perpendicular height is the shortest distance from the base to the opposite side or vertex, meeting the base direction at a right angle. A sloping edge is not the height unless it is perpendicular. For reverse problems, undo multiplication: a rectangle with area 63 cm² and width 7 cm has length 9 cm. For a triangle, double the area before dividing by the base; an area of 35 cm² with base 10 cm gives a height of 7 cm. A parallelogram needs no doubling.
Where area calculations go wrong
| Trap | How to reject it |
|---|---|
| Adding side lengths or finding the perimeter | Area counts surface, so it comes from multiplying perpendicular lengths. A boundary calculation produces linear units and answers a different question. |
| Forgetting the half for a triangle | A triangle occupies half the matching parallelogram or rectangle built from the same base and perpendicular height. Halve the product once. |
| Halving a parallelogram | A parallelogram uses the full base-times-height product. The half belongs to the triangle formula, not to every sloping shape. |
| Using the wrong inverse operation | When area and one perpendicular length are known, divide to recover the other. For a triangle, first account for the half by doubling the area. |
| Keeping plain length units after multiplying two lengths | Multiplying metres by metres or centimetres by centimetres produces a two-dimensional unit such as m² or cm². The unit must describe a surface, not a distance. |
Try it
A square has sides of 6 centimetres. Enter the number of square centimetres in its area.
A right-angled triangle has its two perpendicular sides measuring 5 centimetres and 12 centimetres. Select all the statements that are true about this triangle.
- Its area is 30 square centimetres.
- It covers half as much as a rectangle measuring 5 centimetres by 12 centimetres.
- Its area is 60 square centimetres.
- Its area cannot be found without knowing the length of its longest side.
A parallelogram has a base of 10 centimetres, a slanted side of 7 centimetres and a perpendicular height of 6 centimetres. What is its area?
- 30 square centimetres
- 42 square centimetres
- 60 square centimetres
- 70 square centimetres