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Perimeter and Area - Worksheets, Questions and Revision

20 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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This topic is chapter 5 of KS2 Maths: Measurement Practice Book.

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KS2 · Perimeter and Area

7.6 Perimeter and Area

Calculators not allowed · about 45 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A rectangle has length 12 cm and width 5 cm. Work out its perimeter.
(1)
2
A rectangle floor is 8 squares by 5 squares. A cupboard covers 2 squares by 3 squares in one corner. How many 1 cm by 1 cm squares of floor are left around the cupboard?
(2)
3
A rectangle has length 24 cm and width 2 cm. What is its perimeter?
(1)
4
A rectangle is 9 cm long and 6 cm wide. Work out its area in square centimetres.
(1)
5
A rectangle is 7 cm by 5 cm. The length is increased by 3 cm. Find the new perimeter.
(2)
6
Explain whether two different shapes can have the same perimeter but different areas. Give an example or a reason.
(2)
7
On a 1 cm grid a 4 by 4 square has one corner square removed. What is the area of the remaining shape in square centimetres?
(2)
8
A rectilinear shape has three known side lengths on the outer boundary: 6 cm, 3 cm and 4 cm. The other three outer sides are equal in length. The perimeter is 30 cm. Find the length of each of the three equal sides.
(2)
9
A rectangle measures 6 cm by 4 cm. A boarder 1 cm wide is added all the way around (outside the rectangle). What is the new perimeter of the larger rectangle?
(2)
10
A hall measures 3 m by 4 m. School tiles are 1 m by 1 m squares. How many tiles are needed to cover the whole hall? Show your working.
(2)
11
A rectangle has area 24 cm2 and one side is 6 cm. Find the length of the other side.
(1)
12
A square has side length 9 cm. Write down its perimeter.
(1)
13
Two rectangles are shown. Rectangle A is 6 cm by 3 cm. Rectangle B is 7 cm by 2 cm. Which rectangle has the larger area and which has the larger perimeter? Show working to justify both answers.
(3)
14
The perimeter of a rectangle is 30 cm. One side is 8 cm. Work out the length of the other side.
(2)
15
Find the perimeter of the L-shaped figure on a 1 cm square grid. The shape is made from a 5 by 4 rectangle with a 2 by 2 square removed from one corner. Give your answer in centimetres.
(2)
16
A rectangle on a square grid measures 7 squares by 3 squares. What is its area in square centimetres if each small square is 1 cm by 1 cm?
(1)
17
A shape on a 1 cm grid is made from two rectangles. One is 4 by 3 and the other is 3 by 2. They are joined edge to edge with no overlap, along an edge of length 2 cm. Work out the area of the combined shape in square centimetres.
(2)
18
A 3 by 5 rectangle and a 4 by 4 square both use 1 cm squares. Explain whether they could have the same area. Give a reason for your answer.
(2)
19
On a 1 cm grid, a shape has outer edge lengths 6, 2, 3, 1, 4 and 3 cm in order around the shape. Find the perimeter of the shape.
(2)
20
A square has area 49 cm2. What is the length of one side of the square?
(1)
Mark scheme · 7.6 Perimeter and Area

Question 1

  • B1 Perimeter 34 cm cao
  • Answer: 34 cm

Question 2

  • M1 Correctly find floor area 8x5 = 40 and cupboard area 2x3 = 6
  • B1 34 cm2 cao
  • Answer: 34 cm2

Question 3

  • B1 52 cm cao
  • Answer: 52 cm

Question 4

  • B1 54 cm2 cao
  • Answer: 54 cm2

Question 5

  • M1 Correct new length 10 and method to calculate perimeter 2x(10+5)
  • B1 30 cm cao
  • Answer: 30 cm

Question 6

  • B1 Statement that shapes can have same perimeter but different areas
  • B1 Reason or example e.g. 6x2 rectangle (area 12) and 4x3 rectangle (area 12) is equal area example is acceptable; better example: 5x3 (area 15) and 6x2 (area 12) with same perimeter 16 shows different areas
  • Answer: Yes. For example, a 6 by 2 rectangle and a 5 by 3 rectangle both have perimeter 16 cm, but areas 12 cm2 and 15 cm2 so areas differ.

Question 7

  • M1 Correct method 4x4 = 16 then subtract 1
  • B1 15 cm2 cao
  • Answer: 15 cm2

Question 8

  • M1 Method: subtract known sides 6+3+4 = 13 from 30 to get 17, then divide by 3
  • B1 Each equal side is 17/3 cm or 5 2/3 cm cao
  • Answer: 5 2/3 cm

Question 9

  • M1 New dimensions 8 by 6 found by adding 1 cm each side to length and width
  • B1 Perimeter 28 cm cao
  • Answer: 28 cm

Question 10

  • M1 Method to multiply 3 x 4 to find area in square metres
  • B1 12 tiles cao
  • Answer: 12

Question 11

  • B1 4 cm cao
  • Answer: 4 cm

Question 12

  • B1 Perimeter 36 cm cao
  • Answer: 36 cm

Question 13

  • M1 Correct area calculations: A = 6x3 = 18 and B = 7x2 = 14, or equivalent
  • M1 Correct perimeter calculations: Perimeter A = 2x(6+3) = 18 and Perimeter B = 2x(7+2) = 18
  • B1 Answer stating A has larger area (18 > 14) and perimeters are equal (18 cm) cao
  • Answer: Rectangle A has larger area; both have equal perimeter 18 cm.

Question 14

  • M1 Method to halve 30 and subtract 8, or show 2x + 2*8 = 30 then solve for x
  • B1 7 cm cao
  • Answer: 7 cm

Question 15

  • M1 Correct method to follow outer edges or add side lengths of the L shape
  • B1 Perimeter 18 cm cao
  • Answer: 18 cm

Question 16

  • B1 21 cm2 cao
  • Answer: 21 cm2

Question 17

  • M1 Method adding areas 4x3 + 3x2 or 12 + 6 (no overlap to subtract, as the rectangles only share a boundary edge)
  • B1 18 cm2 cao
  • Answer: 18 cm2

Question 18

  • B1 Correct statement about areas: 3x5 = 15 and 4x4 = 16
  • B1 Reason that areas are not the same because 15 is not equal to 16 cao
  • Answer: No. 3x5 = 15 cm2 and 4x4 = 16 cm2, so the areas are different.

Question 19

  • M1 Correct method to add the given side lengths
  • B1 Perimeter 19 cm cao
  • Answer: 19 cm

Question 20

  • B1 7 cm cao
  • Answer: 7 cm

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