Area, perimeter and volume are easy marks lost to two things: using the wrong formula, and giving the answer in the wrong units.
The maths itself is rarely the problem. The reading and the units are.
Maths carries 25% of the marks, according to the partnership entrance test page. Almost all of it arrives as worded problems rather than bare calculations, which is the part that catches children out.
The formulas worth memorising
| Shape | What to work out | Formula |
|---|---|---|
| Rectangle | Area | length times width |
| Rectangle | Perimeter | 2 times (length plus width) |
| Triangle | Area | half times base times height |
| Square | Area | side times side |
| Cuboid | Volume | length times width times height |
| Cuboid | Surface area | add the areas of all six faces |
Six formulas. A child who knows these cold has the whole topic, and recall needs to be instant rather than reconstructed under time pressure.
Units, where the easy marks go
This catches more children than any calculation does.
- Perimeter is a length, so centimetres: cm.
- Area is a surface, so square centimetres: cm squared.
- Volume is a solid, so cubic centimetres: cm cubed.
And check the question for mixed units. If one side is given in metres and another in centimetres, convert before calculating, not after. Doing it afterwards is how a factor of a hundred goes missing.
Compound shapes: split, do not stare
Most area questions in this test are not plain rectangles. They are L-shapes and rectangles with a bite taken out.
An L-shaped room is a 10 cm by 6 cm rectangle with a 4 cm by 3 cm corner removed. What is its area?
- The whole rectangle: 10 times 6 is 60.
- The removed corner: 4 times 3 is 12.
- The L-shape: 60 minus 12 is 48 cm squared.
Either split the shape into rectangles and add, or complete it to a big rectangle and subtract. Both work. Choose whichever gives the simpler numbers, and draw the split line on the diagram so you can see what you are doing.
The perimeter trap in compound shapes
Here is the error I would most like to prevent.
Taking a bite out of a rectangle reduces its area. It usually does not reduce its perimeter, because the two new edges you create replace the two you removed.
So a child who confidently subtracts from the perimeter the way they subtracted from the area gets it wrong. For perimeter, there is no shortcut: go round the outside edge by edge and add up every side, marking each one off as you go.
Volume and missing sides
Volume questions are often reversed: you are told the volume and two sides, and asked for the third.
If a cuboid has a volume of 60 cm cubed with a base of 5 cm by 4 cm, then 5 times 4 is 20, and 60 divided by 20 is 3 cm.
Same formula, rearranged. Children who have only ever used it forwards freeze here, so practise it backwards deliberately.
See our guide to 11+ maths topics.
See where your child stands today
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Recall has to be automatic, not reconstructed
This is a topic where the mathematics is rarely the obstacle. A child who loses marks here usually understood the shape perfectly well and either reached for the wrong formula or gave the answer in the wrong units.
That is a recall problem, not an understanding problem, and it has a practical fix. Through our tutoring we always give every student a formula sheet in the form of a mind map and get them to memorise it in a set format, so that when it comes to applying it they can recall the right formula without stopping to work it out.
The reason that matters is speed. The speed of answering questions is what causes a lot of children to make mistakes and get lower marks in mathematics, because they cannot work out what is being asked and then decide which formula applies quickly enough. Take the recall off their plate and all of that thinking time goes back into reading the question properly.
Mushtaque Ahmed, Founder of GrammarPath and Bright Mentors
Frequently asked questions
What area and perimeter formulas does my child need for the 11+?
Six: rectangle area is length times width, rectangle perimeter is twice the length plus width, triangle area is half the base times the height, square area is side times side, cuboid volume is length times width times height, and cuboid surface area is the sum of all six faces.
How do you find the area of a compound shape?
Split it into rectangles and add, or complete it to a larger rectangle and subtract. An L-shape made from a 10 by 6 rectangle with a 4 by 3 corner removed has an area of 60 minus 12, which is 48 square centimetres.
Does cutting a corner out of a rectangle reduce its perimeter?
Usually not, and this is a common trap. Removing a corner reduces the area, but the two new edges created replace the two removed, so the perimeter is often unchanged. For perimeter there is no shortcut: go round the outside edge by edge and add every side.
What units should an 11+ answer use?
Perimeter is a length so it uses centimetres, area is a surface so it uses square centimetres, and volume is a solid so it uses cubic centimetres. If the question mixes metres and centimetres, convert before calculating rather than afterwards.
How do you find a missing side from a volume?
Rearrange the formula. If a cuboid has a volume of 60 cubic centimetres and a base of 5 by 4, then 5 times 4 is 20 and 60 divided by 20 gives a height of 3 centimetres. Children who have only used the formula forwards find this hard, so practise it backwards deliberately.