Perimeter, area and volume · Ages 9–10

Perimeter of composite shapes worksheet

Part of: Perimeter and area

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Perimeter, area and volume · Ages 9–10

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Lengths are in cm. What is the perimeter of this shape in cm?
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2.A square's perimeter is 96 cm. How long is each side, in cm?
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3.A square's perimeter is 12 cm. How long is each side, in cm?
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4.A square's perimeter is 92 cm. How long is each side, in cm?
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5.Lengths are in cm, and two sides have no length marked. What is the perimeter of the shape in cm?
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6.How long is the side marked ?, in cm?
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7.A rectangle's perimeter is 90 cm and its length is 25 cm. How wide is it, in cm?
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8.A rectangle's perimeter is 52 cm and its length is 23 cm. How wide is it, in cm?
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9.A rectangle's perimeter is 32 cm and its length is 12 cm. How wide is it, in cm?
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13.Two cards 17 cm by 10 cm are joined along their short sides into one long card. What is the long card's perimeter in cm?
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14.A rectangular playground has a perimeter of 228 m and is 68 m long. How wide is it, in m?
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15.A rectangular table is 110 cm long and 100 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?
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16.Two rectangular sheets, each 20 cm long and 15 cm wide. The second lies on the first, moved 5 cm right and 6 cm down (see the picture). What is the perimeter of the shape they make, in cm?
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17.The picture shows an L-shaped flower bed (lengths in m). How many metres of fence go all round it?
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18.Ka-lok bends a 36 cm wire into a square, using it all. How long is each side, in cm?
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Show the answers and working

Perimeter of composite shapes worksheet: Answers and working

1. 48 cm
All six sides are marked. Start at a corner and add them one by one as you go round.
Add all six sides: 48 cm.
2. 24 cm
A square has four equal sides, which together make 96 cm.
A square's four sides are equal: 96 ÷ 4 = 24.
3. 3 cm
A square has four equal sides, which together make 12 cm.
A square's four sides are equal: 12 ÷ 4 = 3.
4. 23 cm
A square has four equal sides, which together make 92 cm.
A square's four sides are equal: 92 ÷ 4 = 23.
5. 48 cm
Find the unmarked sides from those opposite: the two top pieces together equal the bottom, 11.
The two top pieces equal the bottom, 11, and the two right pieces equal the left, 13: 2 × (11 + 13) = 48.
6. 7 cm
The two top pieces together are as long as which side?
The two top pieces make the bottom: ? = bottom − top piece = 7.
7. 20 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: 90 ÷ 2 = 45, so the width is 45 − 25 = 20.
8. 3 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: 52 ÷ 2 = 26, so the width is 26 − 23 = 3.
9. 4 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: 32 ÷ 2 = 16, so the width is 16 − 12 = 4.

10. C. 52
Picture the big rectangle first: joined along the long sides, what are its length and width? The shared edge doesn't count.
The big rectangle is 14 cm by 2 × 6 cm: 2 × (14 + 2 × 6) = 52.
11. B. 54
Picture the big rectangle first: joined along the long sides, what are its length and width? The shared edge doesn't count.
The big rectangle is 17 cm by 2 × 5 cm: 2 × (17 + 2 × 5) = 54.
12. C. 60
Picture the big rectangle first: joined along the long sides, what are its length and width? The shared edge doesn't count.
The big rectangle is 20 cm by 2 × 5 cm: 2 × (20 + 2 × 5) = 60.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 88 cm
Joined along the short sides, the lengths add up and the width stays. Write down the long card's length and width first.
Joined, it is 2 × 17 cm long and 10 cm wide: 2 × (2 × 17 + 10) = 88.
14. 46 m
The perimeter is two lengths and two widths. First find one length plus one width: half of 228.
228 ÷ 2 − 68 = 46.
15. 20 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 110 cm, so the board is 110 − 100 = 10 cm wide. The perimeter goes from 420 cm to 4 × 110 = 440 cm: 20 cm more.
16. 92 cm
Walk round the outside: the overlap's sides are inside, so they don't count. Find the overlap's length and width first.
Each sheet's perimeter is 70 cm. The overlap is 15 cm by 9 cm, and its four sides lie inside the shape, not round it: 70 + 70 − 2 × (15 + 9) = 92 cm.
17. 46 m
The fence is the perimeter. Find the unmarked sides from those opposite: the two top pieces make the bottom.
Work out the two unmarked sides from those opposite: 2 × (9 + 14) = 46 m.
18. 9 cm
The wire's length is the square's perimeter, and a square's four sides are equal.
The wire's length is the perimeter: 36 ÷ 4 = 9.

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