A rectangle has length 12 cm and width 5 cm. Work out its perimeter.
(1)
2
A square has side length 9 cm. Write down its perimeter.
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3
The perimeter of a rectangle is 30 cm. One side is 8 cm. Work out the length of the other side.
(2)
4
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)
5
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)
6
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)
7
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)
8
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.
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9
A square has area 49 cm2. What is the length of one side of the square?
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10
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)
11
A rectangle has length 24 cm and width 2 cm. What is its perimeter?
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12
A rectangle is 9 cm long and 6 cm wide. Work out its area in square centimetres.
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13
A rectangle is 7 cm by 5 cm. The length is increased by 3 cm. Find the new perimeter.
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14
Explain whether two different shapes can have the same perimeter but different areas. Give an example or a reason.
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15
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)
16
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.
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17
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?
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18
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)
19
A rectangle has area 24 cm2 and one side is 6 cm. Find the length of the other side.
(1)
20
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)
Mark scheme · KS2.M-Y4M2 Perimeter and Area
Question 1
B1 Perimeter 34 cm cao
Answer: 34 cm
Question 2
B1 Perimeter 36 cm cao
Answer: 36 cm
Question 3
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 4
M1 Correct method to follow outer edges or add side lengths of the L shape
B1 Perimeter 18 cm cao
Answer: 18 cm
Question 5
B1 21 cm2 cao
Answer: 21 cm2
Question 6
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 7
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 8
M1 Correct method to add the given side lengths
B1 Perimeter 19 cm cao
Answer: 19 cm
Question 9
B1 7 cm cao
Answer: 7 cm
Question 10
M1 Correctly find floor area 8x5 = 40 and cupboard area 2x3 = 6
B1 34 cm2 cao
Answer: 34 cm2
Question 11
B1 52 cm cao
Answer: 52 cm
Question 12
B1 54 cm2 cao
Answer: 54 cm2
Question 13
M1 Correct new length 10 and method to calculate perimeter 2x(10+5)
B1 30 cm cao
Answer: 30 cm
Question 14
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 15
M1 Correct method 4x4 = 16 then subtract 1
B1 15 cm2 cao
Answer: 15 cm2
Question 16
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 17
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 18
M1 Method to multiply 3 x 4 to find area in square metres
B1 12 tiles cao
Answer: 12
Question 19
B1 4 cm cao
Answer: 4 cm
Question 20
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.