Area and perimeter
Perimeter, area and volume of rectangles, triangles and boxes, plus the coordinates and map scales Rush asks with them: what each question wants, the quick way to answer it, and the traps the wrong answers set.
Chapter 1
What are area and perimeter questions?
You get a shape with its sides measured: a rectangle, a triangle or a box. The question asks how far it is round the edge, how much flat space it covers, or how much it holds.
The shape. Its sides are given in cm or m. Drawings are marked “not to scale”, so use the numbers, never a ruler.
What it asks for. Perimeter, area or volume. The unit gives it away: cm, cm² or cm³.
Rush’s Shapes & Space game also asks about coordinates, mirror lines and map scales. Chapter 4 covers those.
A rectangle is 26 cm long and 10 cm wide. Perimeter in cm?
The options
- Option 1: 62
- Option 2: 72
- Option 3: 260
- Option 4: 36
A Maths question from Rush, level 1.
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Perimeter: round the edge
The distance all the way round, in cm. Add every side: 4 + 3 + 4 + 3 = 14 cm.
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Area: squares inside
How many 1 cm squares cover it, in cm², square centimetres. 3 rows of 4: 4 × 3 = 12 cm².
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Volume: cubes inside
How many 1 cm cubes fill a box, in cm³, cubic centimetres. 2 layers of 12: 24 cm³.
Chapter 2
Solve it in 4 steps.
Here’s the question, one step at a time.
The question
A rectangle is 26 cm long and 10 cm wide. Perimeter in cm?
The options
- Option 1: 62
- Option 2: 72
- Option 3: 260
- Option 4: 36
A Maths question from Rush, level 1.
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Step 1
Read what it asks for.
Perimeter, in cm: the distance round the edge. So you add sides, never multiply them. Draw it and write all four sides on: a rectangle’s opposite sides match.
Opposite sides match.
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Step 2
Add one length and one width.
26 + 10 = 36. That takes you from one corner to the opposite corner: halfway round. 36 is one of the options, waiting for anyone who stops here.
26 + 10 = 36, halfway round.
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Step 3
Double it.
The other length and width are the same again, so the other half is 36 too. 36 × 2 = 72.
36 + 36 = 72.
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Step 4
Check: four sides, once each.
26 + 10 + 26 + 10 = 72. Count the numbers you added. A rectangle has four sides, so it needs four numbers. Three means a side went missing.
Four sides, four numbers.
Three mistakes this question sets
| The mistake | Do this instead |
|---|---|
| Finding the area. 260 is 26 × 10: the squares inside, not the edge. | cm means a length. Add the sides. |
| Stopping halfway. 36 is 26 + 10: one length and one width. | Double it for the other half. |
| Missing a side. 62 is 26 + 26 + 10: only three sides. | Count the numbers: four sides, four numbers. |
So it’s 72 cm. 26 + 10 + 26 + 10: every side once, all the way round.
Remember: The edge adds. The inside multiplies.
Chapter 3
Everything else about area.
Each card is one more kind of question in Shapes & Space: the rule, an example and its trap.
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Area of a rectangle
Length × width, in cm².
8 cm by 3 cm is 3 rows of 8 squares: 8 × 3 = 24 cm². Traps: 22, the perimeter; 11, the sides added; 32, a row too many. For a square, find the side first: a perimeter of 28 cm means sides of 7 cm, so 7 × 7 = 49 cm².
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Half of 48 is 24: one length and one width.
The missing side: halve first
Half the perimeter is one length and one width.
Perimeter 48 cm, 14 cm long: 48 ÷ 2 = 24, and 24 − 14 = 10 cm wide. Traps: 24, stopping at half; 34, from 48 − 14; 20, both widths together.
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Triangles: half a rectangle
Base × height, then halve.
The two light pieces fit together into a second triangle, so the triangle is half of 8 × 7. Halve the even number first: 4 × 7 = 28 cm². Traps: 56, not halved; 15, added; 14, halved twice. The height goes straight up from the base, never along a sloping side.
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Volume: count the layers
Length × width × height, in cm³.
5 cm by 3 cm by 2 cm: each layer is 5 × 3 = 15 cubes, and 2 layers make 30 cm³. Traps: 10, the three added; 15, one layer; 45, a layer too many.
Chapter 4
Coordinates, mirrors and maps.
More than half of the Shapes & Space game is these four kinds.
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Coordinates: across, then up
The first number goes across, the second goes up.
(4, 2) is 4 across and 2 up. Moving left or right changes the first number; up or down, the second. So (4, 2) moved 2 left and 3 up is (2, 5). Trap: the numbers swapped, like (5, 2).
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The missing corner
A rectangle uses each across number twice, and each up number twice.
Corners at (2, 1), (7, 1) and (7, 4). Across, the 2 has no partner. Up, the 4 has none. So the fourth corner is (2, 4). Traps: (7, 4), a corner you were given, and (4, 2), swapped.
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Reflecting in a mirror line
Count the squares to the line, then the same number past it.
X is 2 squares left of the line, so it lands 2 squares right of it, in the same row: B. Traps: C and A are one square out, and D is in the wrong row. A slanting line works the same way: cross it at a right angle.
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Map scales: multiply
Every cm on the map stands for the same distance.
1 cm stands for 20 km, so 6 cm is 6 × 20 = 120 km. Traps: 26, from adding 6 and 20, and 1200, ten times too big. Going back from km to cm, divide: 200 km at 25 km to the cm is 200 ÷ 25 = 8 cm.
In the exam: all four quadrants
Left of 0, the across number is negative. Below 0, the up number is.
The exam’s grid can go past 0 both ways, so (−3, 2) is 3 left of 0 and 2 up. Sliding a point or shape without turning it is a translation, and it works as before: (−3, 2) moved 4 right is (1, 2), because −3 + 4 = 1. Trap: (7, 2), from dropping the minus and doing 3 + 4.
- (−3, 2), 4 right
- −3 + 4 = 1
- (1, 2)
Chapter 5: In the exam
Shapes made of rectangles.
Papers draw L-shapes with some sides left blank. Rush doesn’t ask these, but each one is just two rectangles.
What is the area of this shape, in cm²?
A 34B 52C 68D 70E 28
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Step 1
Find the missing sides.
Across, the bottom is 10 and the top is 4, so the step is 10 − 4 = 6. Up, 7 − 4 = 3.
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Step 2
Split it into two rectangles.
Cut straight down from the step: 4 × 7 = 28 and 6 × 4 = 24. 28 + 24 = 52.
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Step 3
Check another way.
The whole 10 by 7 rectangle is 70. Take away the missing corner, 6 × 3 = 18: 70 − 18 = 52.
Three mistakes it sets
| The mistake | Do this instead |
|---|---|
| Forgetting the corner. 70 cm² (D) is the whole 10 by 7 rectangle. | Take the missing corner away. |
| Counting a piece twice. 68 cm² (C) is 4 × 7 plus 10 × 4. The bottom-left 4 by 4 square is in both. | Cut so the pieces don’t overlap. |
| Adding the sides. 34 (A) is the perimeter, a length. | cm² means squares inside: multiply. |
So it’s 52 cm², B. Two rectangles, 28 + 24. And 70 − 18 agrees.
Remember: Missing sides first, then split.
Other ways the exam asks it
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The perimeter of an L-shape
Find the blank sides first (2 and 3), then add all six, ticking each one off: 30 cm. Trap: 25, only the four labelled sides. A corner cut out leaves the perimeter the same as the full rectangle’s: 9 + 6 + 9 + 6 = 30.
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Working backwards
Area 24 cm², width 4 cm: how long? Undo the times with a divide: 24 ÷ 4 = 6 cm. Trap: 20, from 24 − 4. Boxes work the same way: 120 cm³ on a 4 by 5 base is 120 ÷ 20 = 6 cm high.
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Metres and centimetres
Make the units match before you multiply. A path 2 m long and 30 cm wide is 200 × 30 = 6000 cm². Trap: 60, from 2 × 30. And 1 m² is 100 × 100 = 10,000 cm², not 100.
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How many tiles?
A wall 60 cm by 40 cm, with square tiles 10 cm wide. Count along each side: 6 across, 4 up, so 6 × 4 = 24 tiles. Trap: 240, from dividing the area by 10, not by the tile’s area, 100.
Chapter 6
Try it yourself.
Six real questions from Rush, easy to hard, 60 seconds on the clock.
Use the steps
- Read what it asks for.
- Add one length and one width.
- Double it.
- Check: four sides, once each.
Remember: The edge adds. The inside multiplies.
For parents.
What parents ask us about area and perimeter.
Questions parents ask
What's the difference between area and perimeter?
Perimeter is the distance round the outside, measured in cm or m. Area is how much surface the shape covers, counted in squares: cm² or m². A 6 by 4 rectangle has a perimeter of 20 cm and an area of 24 cm², so the same shape gives two different numbers.
How do I stop my child mixing up area and perimeter?
Both use the same two numbers, and the wrong options come from mixing them up. Ask your child to say the unit out loud before starting: 'cm' means walk round the edge, 'cm squared' means fill it with squares.
How do you find the area of a triangle?
Halve the base or the height, whichever is even, then multiply. It's easier to remember why than to remember the formula: every triangle is half of the rectangle drawn round it. Halving the even number first keeps the multiplication small.
Do 11+ maths papers ask about volume?
Volume of a cuboid is on the Year 6 curriculum, so papers can ask it, as a cuboid or a shape built from cubes. Volume is length × width × height, in cm³. Thinking in layers helps: the bottom layer is length × width cubes, and there are as many layers as the height.
Rush: 11+ Practice & KS2 SATsPractise area and perimeter in Rush.
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