A rectangle has length 8 m and width 3 m. Work out its area.
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2
A garden bed is a rectangle 250 cm long and 120 cm wide. What is the area in square centimetres?
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3
Write down the perimeter of a rectangle with sides 7 cm and 5 cm.
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4
A classroom carpet is made from two rectangles joined along their short side. One rectangle is 4 m by 3 m, the other is 4 m by 2 m. Calculate the total area of the carpet.
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5
A rectangular water tray holds 6 layers of cubes. Each layer is 5 cubes long and 3 cubes wide. How many cubes fit in the tray altogether?
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6
A rectangle has area 48 cm2 and one side is 6 cm. Work out the length of the other side.
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7
A border around a square flower bed is 1 m wide. The outside edge of the border makes a larger square 8 m by 8 m. What is the area of the flower bed (the inner square)?
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8
Estimate the area of this irregular shape by counting full 1 cm by 1 cm squares and sensible halves. The shape covers 7 full squares and 5 half squares.
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9
A storage box is 40 cm by 30 cm by 20 cm. A small cube has side 10 cm. What is the largest number of small cubes that can fit into the box without breaking them?
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10
A rectangle has perimeter 30 m. One side is 8 m. Work out the length of the opposite side.
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11
Sana builds a tower with cubes. The base layer is 6 cubes by 2 cubes. She stacks 4 identical layers. How many cubes are in the tower? Show your working.
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12
A playground has a rectangular patch of sand 9 m by 4 m. A square seesaw area of 2 m by 2 m is inside the sand. What is the area of sand not covered by the seesaw?
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13
Here is a rectangle 12 cm by 5 cm. A 4 cm by 2 cm rectangle is cut out from one corner. Work out the area of the remaining shape.
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14
Explain why two rectangles with the same area can have different perimeters. Give a short example using whole-number sides.
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15
A fish tank is 60 cm long and 25 cm wide. The base is filled with a layer of stones 5 cm deep made from small cubes of size 5 cm. How many small cubes are needed to make the layer?
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16
A rectangle has length 9 m and area 63 m2. A smaller similar rectangle has length 3 m. What is the area of the smaller rectangle?
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17
A model made from identical small cubes has three layers. The bottom layer is 4 by 3 cubes, the middle is 3 by 3, the top is 2 by 3. How many cubes are in the model? Explain your method.
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18
Estimate the area of a pond drawn on a 1 cm grid where about 13 full squares and 6 quarters are covered. Give your estimate in square centimetres.
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Mark scheme · KS2.M-Y5M2 Perimeter, Area and Volume
Question 1
M1 Multiply length by width or show 8 x 3
B1 24 m2 cao
Answer: 24 m2
Question 2
M1 Multiply 250 x 120 or show correct method
B1 30,000 cm2 cao
Answer: 30000 cm2
Question 3
B1 24 cm cao
Answer: 24 cm
Question 4
M1 Correct area for each rectangle or method shown (4x3 and 4x2)
B1 20 m2 cao
Answer: 20 m2
Question 5
M1 Multiply layer area 5 x 3 = 15 and show times 6
B1 90 cao
Answer: 90
Question 6
M1 Divide 48 by 6 or show correct method
B1 8 cm cao
Answer: 8 cm
Question 7
M1 Subtract border twice from 8 to get inner side 6 (or show 8 - 1 - 1)
B1 36 m2 cao
Answer: 36 m2
Question 8
B1 9.5 cm2 or 9.5 cao
Answer: 9.5 cm2
Question 9
M1 Divide each dimension by 10 to find how many cubes in each direction: 4, 3, 2
B1 24 cao
Answer: 24
Question 10
M1 Use perimeter formula 2(l + w)=30 or show 2 x (8 + w) = 30
B1 7 m cao
Answer: 7 m
Question 11
M1 Find layer area 6 x 2 = 12 and multiply by 4
B1 48 cao
Answer: 48
Question 12
B1 32 m2 cao
Answer: 32 m2
Question 13
M1 Find whole rectangle area 12 x 5 = 60 and subtract cut-out 4 x 2 = 8
B1 52 cm2 cao
Answer: 52 cm2
Question 14
B1 Correct explanation and example, e.g. 6x4 and 8x3 both area 24 but perimeters 20 and 22 respectively, showing why perimeters differ
Answer: Example: 6 and 4 (area 24) and 8 and 3 (area 24); perimeters 20 and 22
Question 15
M1 Compute number across length 60/5 = 12, across width 25/5 = 5, and depth 5/5 = 1 then multiply 12 x 5 x 1
B1 60 cao
Answer: 60
Question 16
M1 Find scale factor for length 3/9 = 1/3 and square it or use area proportionality
B1 7 m2 cao
Answer: 7 m2
Question 17
M1 Add each layer: 12 + 9 + 6 or show correct layer totals