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Perimeter, area, and volume questions appear on both stages of the SET 11+ maths papers. You need to know the formulas, apply them to a range of shapes, and — especially on Stage 2 — show every step of your working. This lesson covers all the key formulas and gives you plenty of worked examples.
The perimeter is the total distance around the outside of a shape.
Perimeter = 2 × (length + width)
Example: A rectangle is 12 cm long and 7 cm wide.
For compound (L-shaped or T-shaped) shapes, add up all the outer edges. You may need to work out missing lengths first.
Area is the amount of surface a shape covers. It is measured in square units (cm², m²).
| Shape | Formula |
|---|---|
| Rectangle | length × width |
| Triangle | 1/2 × base × height |
| Parallelogram | base × height |
| Trapezium | 1/2 × (a + b) × height |
| Circle | pi × radius × radius |
Note: For SET 11+ questions involving circles, use pi = 3.14 or pi = 22/7 (the question will usually tell you which to use).
Find the area of a triangle with base 16 cm and height 9 cm.
Find the area of a trapezium with parallel sides 8 cm and 14 cm, and height 6 cm.
An L-shape is made of two rectangles. The overall shape is 10 cm wide and 8 cm tall. The notch cut out of the top-right is 4 cm wide and 3 cm tall. Find the area.
Method 1 (subtract):
Volume is the amount of space inside a 3D shape. It is measured in cubic units (cm³, m³).
| Shape | Formula |
|---|---|
| Cuboid | length × width × height |
| Cube | side × side × side |
| Triangular prism | area of cross-section × length |
| Cylinder | pi × radius × radius × height |
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