Perimeter, area and volume · Ages 9–10

Area of composite shapes worksheet

Part of: Perimeter and area

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Perimeter, area and volume · Ages 9–10

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

1.A square's area is 9 cm². How long is each side, in cm?
Answer:
2.A rectangle's area is 117 cm² and its length is 13 cm. How wide is it, in cm?
Answer:
3.A rectangle's area is 70 cm² and its length is 14 cm. How wide is it, in cm?
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4.A square's area is 100 cm². How long is each side, in cm?
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5.Lengths are in cm. What is the area of this shape in cm²?
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6.Lengths are in cm, and two sides have no length marked. What is the area of the shape in cm²?
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7.A card 17 cm by 15 cm has a window 2 cm by 3 cm cut from its middle. What area of card is left, in cm²?
Answer:
8.A card 20 cm by 12 cm has a window 2 cm by 4 cm cut from its middle. What area of card is left, in cm²?
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13.A rectangular wall is 6 m long and 4 m high, with a window 3 m wide and 2 m high. The window isn't painted. What area is painted, in m²?
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14.A rectangular table is 90 cm long and 70 cm wide. A rectangular board is added along one long side, making a square table. What is the area of the board, in cm²?
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15.The picture shows an L-shaped living room (lengths in m) to be floored. What area of flooring is needed, in m²?
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16.A rectangular vegetable plot has an area of 133 m² and is 7 m wide. How many metres of wire fence go all round it?
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17.Two rectangular sheets, each 13 cm long and 12 cm wide. The second lies on the first, moved 10 cm right and 10 cm down (see the picture). How many cm² do the two sheets cover altogether?
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18.A rectangular table is 100 cm long and 80 cm wide. A rectangular board is added along one long side, making a square table. What is the area of the board, in cm²?
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Show the answers and working

Area of composite shapes worksheet: Answers and working

1. 3 cm
A square's area is side × side. Which number times itself makes 9?
Side × side = 9: 3 × 3 = 9, so the side is 3 cm.
2. 9 cm
Length × width = area. You know the area, 117, and the length, 13: how do you find the width?
Length × width = area, so the width is 117 ÷ 13 = 9.
3. 5 cm
Length × width = area. You know the area, 70, and the length, 14: how do you find the width?
Length × width = area, so the width is 70 ÷ 14 = 5.
4. 10 cm
A square's area is side × side. Which number times itself makes 100?
Side × side = 100: 10 × 10 = 100, so the side is 10 cm.
5. 33 cm²
Think of it as a 9 × 5 rectangle with a corner missing. Work out the big rectangle first, then deal with the gap.
The big rectangle 9 × 5, less the missing 4 × 3: 33 cm².
6. 119 cm²
The gap's two sides aren't marked. Work out how wide and how tall the gap is from the sides opposite first.
First the gap: its width is bottom − top, its height left − right. Then the big rectangle less the gap: 119.
7. 249 cm²
The card left is the whole card less the window. Find each rectangle's area first.
17 × 15 − 2 × 3 = 249.
8. 232 cm²
The card left is the whole card less the window. Find each rectangle's area first.
20 × 12 − 2 × 4 = 232.

9. True
It's a 11 × 14 rectangle with a corner missing. Check whether 145 has the gap subtracted.
The big rectangle 11 × 14 less the gap 3 × 3: 145 cm².
10. A. 15 × 11 + 6 × 2
Cut across along the bottom of the gap, then find the length and width of each of the two pieces.
The bottom piece is 15 × 11 and the top piece 6 × 2: add them.
11. False
It's a 9 × 10 rectangle with a corner missing. Check whether 90 has the gap subtracted.
The big rectangle 9 × 10 less the gap 7 × 8: 34 cm².
12. False
It's a 7 × 12 rectangle with a corner missing. Check whether 84 has the gap subtracted.
The big rectangle 7 × 12 less the gap 5 × 2: 74 cm².

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

13. 18 m²
The painted part is the whole wall less the window. Find the wall's and the window's areas first.
6 × 4 − 3 × 2 = 18.
14. 1800 cm²
In the square, every side is as long as the table. How wide must the board be to fill the gap?
Each side of the square is 90 cm, so the board is 90 cm long and 90 − 70 = 20 cm wide: 90 × 20 = 1800 cm².
15. 146 m²
Treat the room as a 12 × 13 rectangle with a corner missing; work out the big rectangle first.
12 × 13 − 2 × 5 = 146 m².
16. 52 m
The fence is the perimeter, but you need the length first: find it from the area, 133, and the width, 7.
Length = 133 ÷ 7 = 19 m, so the perimeter is 2 × (19 + 7) = 52 m.
17. 306 cm²
Adding the two sheets counts the overlap twice. Find the overlap's length and width first.
Each sheet is 13 × 12 = 156 cm². The overlap is 3 cm by 2 cm, 6 cm², counted twice, so take it off once: 156 + 156 − 6 = 306.
18. 2000 cm²
In the square, every side is as long as the table. How wide must the board be to fill the gap?
Each side of the square is 100 cm, so the board is 100 cm long and 100 − 80 = 20 cm wide: 100 × 20 = 2000 cm².

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