Perimeter, area and volume · Ages 9–10
Perimeter and area worksheet
Covers: Counting perimeter, Perimeter of composite shapes, What area is, Counting squares for area, Perimeter and area of rectangles and squares, Area of composite shapes
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Perimeter and area worksheet
Perimeter, area and volume · Ages 9–10
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A rectangle's perimeter is 58 cm and its length is 16 cm. How wide is it, in cm?
Answer:
2.Lengths are in cm, and two sides have no length marked. What is the perimeter of the shape in cm?
Answer:
3.Taking one small square as the unit, how many small squares is this shape's area?
Answer:
4.Each square on the paper is 1 cm². What is the area of the shape in cm²?
Answer:
5.Rectangle, perimeter 16 cm, length 6 cm: width = ? cm
Answer:
6.Square, perimeter 32 cm: side = ? cm
Answer:
7.A rectangle's area is 36 cm² and its length is 12 cm. How wide is it, in cm?
Answer:
8.Lengths are in cm. What is the area of this shape in cm²?
Answer:
Part B: Choose, or true or false (2 marks each)
9.Each square on the paper is 1 cm a side. Which shape has the longest perimeter?
- A
- B
- C
- D
Choose the right picture
Answer:
10.Squares 1 cm a side are laid in 3 rows of 5 to make a rectangle. What is its perimeter?
- A. 8 cm
- B. 20 cm
- C. 15 cm
- D. 16 cm
Choose the right answer
Answer:
11.A table top can be covered exactly by 25 red cards, or exactly by 26 blue cards. Each red card is bigger than each blue card.
True or false?
Answer:
12.Each square on the paper is 1 cm². The shape's area is 13 cm².
True or false?
Answer:
Part C: Word problems (4 marks each)
13.12 square mats 1 m a side are laid as a rectangle in 3 equal rows. What is its perimeter in m?
Working:
Answer:
14.A rectangular table is 140 cm long and 120 cm wide. A board as long as the table is added along one long side, making a square table. How many cm longer is the square table's perimeter than the old one's?
Working:
Answer:
15.A wall takes exactly 4 big posters. Each big poster is the area of 6 small ones. How many small posters does the wall take exactly?
Working:
Answer:
16.Ka-lok covers this shape on squared paper exactly with square stickers 1 cm a side. How many stickers does it take?
Working:
Answer:
17.A square photo frame has a perimeter of 100 cm. How long is each side, in centimetres?
Working:
Answer:
18.A rectangular wall is 12 m long and 5 m high, with a window 2 m wide and 1 m high. The window isn't painted. What area is painted, in m²?
Working:
Answer:
Show the answers and working
Perimeter and area worksheet: Answers and working
Part A: Working out and filling in
1. 13 cm
The perimeter is two lengths and two widths. Find what one length and one width make first.
One length and one width make half the perimeter: 58 ÷ 2 = 29, so the width is 29 − 16 = 13.
2. 44 cm
Find the unmarked sides from those opposite: the two top pieces together equal the bottom, 9.
The two top pieces equal the bottom, 9, and the two right pieces equal the left, 13: 2 × (9 + 13) = 44.
3. 11 small squares
The area is how many small squares the shape takes up. Count column by column, then add.
Column by column: 3 + 4 + 4 = 11, so the area is 11 small squares.
4. 13 cm²
Area counts squares. Count column by column, then add the columns.
Column by column: 2 + 4 + 3 + 4 = 13 squares, so 13 cm².
5. Rectangle, perimeter 16 cm, length 6 cm: width = 2 cm
Half the perimeter is length + width: 16 ÷ 2 = 8, then take the length: 8 − 6 = 2
6. Square, perimeter 32 cm: side = 8 cm
A square has four equal sides: 32 ÷ 4 = 8
7. 3 cm
Length × width = area. You know the area, 36, and the length, 12: how do you find the width?
Length × width = area, so the width is 36 ÷ 12 = 3.
8. 76 cm²
Think of it as a 15 × 6 rectangle with a corner missing. Work out the big rectangle first, then deal with the gap.
The big rectangle 15 × 6, less the missing 7 × 2: 76 cm².
Part B: Choose, or true or false
9. A
Count once round each shape. Where the top steps up or down, each step's upright edge counts too.
Count round each shape's edge: the longest perimeter is 18 cm.
10. D. 16 cm
The rectangle is 5 cm long and 3 cm wide. The perimeter goes all the way round: count all four sides.
5 cm long and 3 cm wide: once round is 5 + 3 + 5 + 3 = 16 cm.
11. True
For the same table top, the more cards it takes, the smaller each card is. See which is more, 25 or 26.
For the same table, the fewer cards it takes, the bigger each card. It takes 25 red or 26 blue; 25 is fewer than 26, so the kind that takes 25 has the bigger cards.
12. True
Area counts squares, not edges. Count the squares column by column and compare with 13.
Area counts squares: 13 of them; 16 is the number of edge pieces, the perimeter.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 14 m
Find how many are in each row first: 12 mats in 3 equal rows.
12 ÷ 3 = 4 a row: 4 m by 3 m, so 2 × (4 + 3) = 14 m.
14. 40 cm
In the square, every side is as long as the table. Find how wide the board must be first.
The square's side is 140 cm, so the board is 140 − 120 = 20 cm wide. The perimeter goes from 520 cm to 4 × 140 = 560 cm: 40 cm more.
15. 24 posters
Change the big posters into small ones first: one big poster is 6 small ones.
Each big poster is 6 small ones: 4 × 6 = 24.
16. 11 stickers
Each sticker covers exactly 1 square, so count the shape's squares, column by column.
Each sticker is one square: count the squares, 11.
17. A square photo frame has a perimeter of 100 cm. How long is each side, in centimetres? (Answer: 25 cm)
100 ÷ 4 = 25
18. 58 m²
The painted part is the whole wall less the window. Find the wall's and the window's areas first.
12 × 5 − 2 × 1 = 58.
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