Area and Perimeter (Part 2) - Worksheets, Questions and Revision

17 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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2.11B Area and Perimeter (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A P.E. teacher is measuring two things at school: the perimeter of the running track and the area of the sports hall floor.

(a)Circle the most sensible unit for measuring the perimeter of the running track.

mm cm m km(1)

(b)Circle the most sensible unit for measuring the area of the sports hall floor.

mm² cm² m² km²(1)

(Total for Question 1 is 2 marks)

The shape below is drawn on a 1 cm square grid, made from whole centimetre squares.

Figure (to be drawn): An L-shaped (bracket-shaped) figure on a 1 cm square grid. The outer bounding rectangle is 5 squares wide and 3 squares tall; a 2-square wide by 2-square tall notch is removed from the top-right corner, leaving an L-shape made of 11 unit squares. Internal grid lines are visible inside the shape so every unit square can be counted.

(a)Find the area of the shape by counting whole squares.(1)

(b)Find the perimeter of the shape by counting the unit lengths along the edge.(1)

(Total for Question 2 is 2 marks)

A rectangular vegetable patch measures 9 m by 4 m.

(a)Work out the perimeter of the vegetable patch.(2)

(b)Work out the area of the vegetable patch.(2)

(Total for Question 3 is 4 marks)

A square rug has a side length of 1.8 m.

(a)Work out the perimeter of the rug.(1)

(b)Work out the area of the rug.(2)

(Total for Question 4 is 3 marks)

To find the area of a rectangle with length 12 cm and width 5 cm, a student wrote:

Area = 12 + 5 = 17 cm²

(a)Explain the mistake in the student's method.(1)

(b)Work out the correct area of the rectangle.(1)

(Total for Question 5 is 2 marks)

A rectangular lawn measures 7.5 m by 4 m.

Show that the area of the lawn is 30 m².

(Total for Question 6 is 2 marks)

A square patio has an area of 49 m².

Work out the perimeter of the patio.

(Total for Question 7 is 3 marks)

A triangular sail has a base of 3.6 m and a perpendicular height of 2.5 m.

Work out the area of the sail.

(Total for Question 8 is 2 marks)

A triangular flag has an area of 24 cm² and a base of 8 cm.

Work out the perpendicular height of the flag.

(Total for Question 9 is 3 marks)

Amara is choosing between two flower beds for her garden.

Flower bed A is rectangular, measuring 5 m by 3 m.
Flower bed B is triangular, with a base of 8 m and a perpendicular height of 4 m.

Which flower bed has the greater area? You must show your working.

(Total for Question 10 is 3 marks)

A patio is L-shaped. It is formed by cutting a 3 m by 2 m rectangle out of one corner of a 9 m by 6 m rectangular patio, to leave space for a tree.

Work out the perimeter of the L-shaped patio.

(Total for Question 11 is 3 marks)

Using the same L-shaped patio as the previous question (a 3 m by 2 m rectangle cut from the corner of a 9 m by 6 m rectangular patio), work out the area of the patio.

(Total for Question 12 is 3 marks)

A rectangular picture frame has a length of 45 cm and a width of 0.3 m.

Work out the perimeter of the frame in centimetres.

(Total for Question 13 is 3 marks)

A garden gate is cut from a rectangular sheet of wood measuring 1.2 m wide and 1.4 m tall. To let the gate swing clear of a sloping path, a right-angled triangular corner is cut off the top of the sheet. The triangular corner removed has a base of 0.6 m and a perpendicular height of 0.4 m.

Work out the area of the gate that remains after the corner is cut off.

(Total for Question 14 is 3 marks)

A rectangular paddock measures 20 m by 15 m. The paddock needs fencing all the way around, except for a 3 m wide gate opening on one of the 20 m sides. Fencing costs 7.25 pounds per metre.

Work out the total cost of the fencing.

(Total for Question 15 is 4 marks)

Mr Whitfield is repainting one wall of the school hall storeroom. The wall measures 6 m by 2.4 m. One tin of paint covers 5 m², and tins can only be bought whole. Each tin costs 18.50 pounds.

(a)Work out the area of the wall.(1)

(b)Work out the number of tins of paint needed.(2)

(c)Work out the total cost of the paint.(1)

(Total for Question 16 is 4 marks)

A classroom floor measures 8 m by 6 m. The school is comparing two ways of covering the floor:

Vinyl flooring costs 9.20 pounds per m².
Carpet tiles are sold in boxes costing 45 pounds each, and each box covers exactly 3 m².

(a)Work out the area of the classroom floor.(1)

(b)Work out the cost of covering the floor with vinyl flooring.(2)

(c)Work out the cost of covering the floor with carpet tiles.(3)

(d)State which type of flooring is cheaper, and work out the difference in cost.(2)

(Total for Question 17 is 8 marks)

Mark scheme · 2.11B Area and Perimeter (Part 2)

Question 1

(a) B1 m circled oe
(a) Answer: m
(b) B1 m² circled oe
(b) Answer: m²

Question 2

(a) B1 11 cao
(a) Answer: 11 cm²
(b) B1 16 cao
(b) Answer: 16 cm

Question 3

(a) M1 9 + 9 + 4 + 4 or 2(9 + 4) oe
(a) A1 26 cao
(a) Answer: 26 m
(b) M1 9 x 4
(b) A1 36 cao
(b) Answer: 36 m²

Question 4

(a) B1 7.2 cao
(a) Answer: 7.2 m
(b) M1 1.8 x 1.8
(b) A1 3.24 cao
(b) Answer: 3.24 m²

Question 5

(a) B1 states the student added the length and width instead of multiplying them oe
(a) Answer: The student added the length and width instead of multiplying them.
(b) B1 60 cao
(b) Answer: 60 cm²

Question 6

M1 7.5 x 4 oe, method shown
A1 30 (cso), dependent on correct working shown
Answer: 30 m² (shown)

Question 7

M1 finds the side length: √49 = 7 oe
M1 4 x 7, ft their side length
A1 28 cao
Answer: 28 m

Question 8

M1 0.5 x 3.6 x 2.5 oe
A1 4.5 cao
Answer: 4.5 m²

Question 9

M1 0.5 x 8 x h = 24 oe
M1 24 x 2 / 8 or 48 / 8 oe
A1 6 cao
Answer: 6 cm

Question 10

M1 5 x 3 = 15
M1 0.5 x 8 x 4 = 16
A1 Flower bed B, since 16 > 15, dependent on both areas correct
Answer: Flower bed B (16 m² compared with 15 m²)

Question 11

M1 6 - 2 = 4 to find the missing shorter side oe
M1 9 - 3 = 6 to find the missing longer side oe
A1 30 cao
Answer: 30 m

Question 12

M1 9 x 6 = 54
M1 3 x 2 = 6
A1 48 cao
Answer: 48 m²

Question 13

M1 0.3 m = 30 cm oe
M1 2 x (45 + 30) oe
A1 150 cao
Answer: 150 cm

Question 14

M1 1.2 x 1.4
M1 0.5 x 0.6 x 0.4
A1 1.56 cao
Answer: 1.56 m²

Question 15

M1 2(20 + 15) = 70 oe
M1 70 - 3 = 67 oe
M1 67 x 7.25, ft their length
A1 485.75 (pounds) cao
Answer: GBP 485.75

Question 16

(a) B1 14.4 cao
(a) Answer: 14.4 m²
(b) M1 14.4 / 5 = 2.88, ft their (a)
(b) A1 3, since tins can only be bought whole and 2 tins (covering 10 m²) would not be enough to cover the wall
(b) Answer: 3 tins
(c) B1 55.50 (pounds), ft their (b)
(c) Answer: GBP 55.50

Question 17

(a) B1 48 cao
(a) Answer: 48 m²
(b) M1 48 x 9.20, ft their (a)
(b) A1 441.60 (pounds) cao
(b) Answer: GBP 441.60
(c) M1 48 / 3 = 16 (boxes), ft their (a)
(c) M1 16 x 45, ft their number of boxes
(c) A1 720 (pounds) cao
(c) Answer: GBP 720
(d) M1 720 - 441.60, ft their (b) and (c)
(d) A1 Vinyl flooring, 278.40 (pounds) cao
(d) Answer: Vinyl flooring, GBP 278.40 cheaper

Question 17

8 marks

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Area and Perimeter (Part 2) - Worksheets, Questions and Revision

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2.11B Area and Perimeter (Part 2)

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