Perimeter, Area and Volume
Perimeter, area and volume are measurements of the size of 2D and 3D shapes: perimeter is the total distance around the outside edge, area is the amount of flat space a shape covers, and volume is the amount of space a 3D solid takes up. 11+ maths papers test these using rectangles, triangles, compound shapes and cuboids, often set in real-life contexts such as fencing or carpeting a room.
Before you start
Make sure you're comfortable with these topics first:
Method
- Sketch or label the shape if one is not already given, marking on all the lengths you know.
- For perimeter, add together the lengths of all the sides; for an L-shape or compound shape, work out any missing side lengths first using the given measurements.
- For area, use the correct formula for the shape: rectangle = length x width, triangle = 0.5 x base x height, parallelogram = base x height, trapezium = 0.5 x (sum of parallel sides) x height.
- For compound shapes, split the shape into simpler rectangles or triangles, find each area separately, then add or subtract to get the total.
- For the volume of a cuboid, multiply length x width x height, making sure every measurement is in the same unit first.
- Always state the correct units: length in cm or m, area in cm^2 or m^2, and volume in cm^3 or m^3.
Worked example
A garden path is L-shaped. It is formed from an 11 cm by 8 cm rectangle with a 4 cm by 3 cm rectangle removed from the top right corner. Calculate (a) the perimeter and (b) the area of the L-shape.
- Find the missing horizontal length: 11 - 4 = 7 cm (the top edge).
- Find the missing vertical length: 8 - 3 = 5 cm (the right-hand edge below the notch).
- Add all six sides of the L-shape: 11 + 5 + 4 + 3 + 7 + 8 = 38 cm. This is the perimeter.
- Find the area of the full outer rectangle: 11 x 8 = 88 cm^2.
- Find the area of the removed rectangle: 4 x 3 = 12 cm^2.
- Subtract: 88 - 12 = 76 cm^2. (a) Perimeter = 38 cm. (b) Area = 76 cm^2.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A trapezium has parallel sides of length 9 cm and 13 cm, and a perpendicular height of 6 cm. Calculate the area of the trapezium.
A solid cuboid measures 12 cm by 9 cm by 5 cm. A smaller cuboid measuring 5 cm by 4 cm by 5 cm is cut out of one vertical edge, running the full height of the solid. Calculate the volume of the remaining solid.
A cuboid storage box has length 45 cm, width 20 cm and height 15 cm. (a) Calculate the volume of the box in cm^3. (b) The box is filled with water until it is 2/5 full. Calculate the volume of water in the box. (c) Given that 1000 cm^3 = 1 litre, calculate how many litres of water this is.
Free printable worksheet
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