Shape and space · Ages 8–9

Parallelograms and trapeziums worksheet

Part of: Parallel lines, quadrilaterals and triangles

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Shape and space · Ages 8–9

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

1.Two neighbouring sides of a parallelogram are 5 cm and 6 cm. How long is the side opposite the 5 cm side?
Answer:
2.Two neighbouring sides of a parallelogram are 11 cm and 9 cm. How long is the side opposite the 11 cm side?
Answer:
3.Two neighbouring sides of a parallelogram are 13 cm and 11 cm. How long is the side opposite the 13 cm side?
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4.Two neighbouring sides of a parallelogram are 18 cm and 10 cm. How long is the side opposite the 18 cm side?
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5.How many pairs of opposite sides of the quadrilateral on the dot paper are parallel?
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13.May makes a parallelogram from four plastic strips. Two neighbouring strips are 29 cm together, and one of them is 9 cm. How long are the four strips altogether?
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14.A board is a trapezium. Its upper base is 40 cm, its lower base is 10 cm longer, and each leg is 5 cm. How long are its four sides altogether?
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15.A flower bed is a parallelogram with neighbouring sides of 4 m and 14 m. How many metres of fence go all the way round it?
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16.A board is a trapezium. Its upper base is 29 cm, its lower base is 8 cm longer, and each leg is 19 cm. How long are its four sides altogether?
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17.Ming makes a parallelogram from four plastic strips. Two neighbouring strips are 28 cm together, and one of them is 16 cm. How long are the four strips altogether?
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18.A flower bed is a parallelogram with neighbouring sides of 9 m and 8 m. How many metres of fence go all the way round it?
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Show the answers and working

Parallelograms and trapeziums worksheet: Answers and working

1. 5 cm
How are a parallelogram's opposite sides related? Find the side opposite the 5 cm one.
A parallelogram's opposite sides are equal: 5 cm.
2. 11 cm
How are a parallelogram's opposite sides related? Find the side opposite the 11 cm one.
A parallelogram's opposite sides are equal: 11 cm.
3. 13 cm
How are a parallelogram's opposite sides related? Find the side opposite the 13 cm one.
A parallelogram's opposite sides are equal: 13 cm.
4. 18 cm
How are a parallelogram's opposite sides related? Find the side opposite the 18 cm one.
A parallelogram's opposite sides are equal: 18 cm.
5. 2 pairs
Compare the moves of the top and bottom sides first, then of the left and right sides.
Opposite sides are parallel when their moves match: 2 pair(s).

6. B. Trapezium
Count each side's squares across and down, then compare the two pairs of opposite sides. How many pairs match?
Count each side's moves: two parallel pairs is a parallelogram, one pair a trapezium, none neither.
7. True
Look at the shape: how many sides does it have, and are both pairs of opposite sides parallel?
Any quadrilateral with two pairs of parallel sides is a parallelogram — squares and rectangles too.
8. A. They are parallel
Think what makes a trapezium: how many pairs of its opposite sides are parallel, and which pair?
A trapezium has exactly one parallel pair: its two bases.
9. C. They are parallel
Think what makes a trapezium: how many pairs of its opposite sides are parallel, and which pair?
A trapezium has exactly one parallel pair: its two bases.
10. C. They are parallel
Think what makes a trapezium: how many pairs of its opposite sides are parallel, and which pair?
A trapezium has exactly one parallel pair: its two bases.
11. A. They are parallel
Think what makes a trapezium: how many pairs of its opposite sides are parallel, and which pair?
A trapezium has exactly one parallel pair: its two bases.
12. A
See how the top side moves from the first corner to the second. The fourth corner is that move backwards from the third.
From the third corner, make the top side's move backwards: 5 squares left.

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

13. 58 cm
Opposite sides are equal, so the four strips make two neighbouring pairs, each 29 cm together.
The other is 20 cm; opposite sides are equal, so all four are 2 × 29 = 58 cm.
14. 100 cm
Find the lower base first: 10 cm longer than the 40 cm upper base. Then add all four sides.
Bottom base 40 + 10 = 50; 40 + 50 + 5 + 5 = 100.
15. 36 m
A parallelogram's opposite sides are equal, so its sides are two of 4 m and two of 14 m.
Opposite sides are equal, so the sides are 4, 14, 4, 14: 36 m.
16. 104 cm
Find the lower base first: 8 cm longer than the 29 cm upper base. Then add all four sides.
Bottom base 29 + 8 = 37; 29 + 37 + 19 + 19 = 104.
17. 56 cm
Opposite sides are equal, so the four strips make two neighbouring pairs, each 28 cm together.
The other is 12 cm; opposite sides are equal, so all four are 2 × 28 = 56 cm.
18. 34 m
A parallelogram's opposite sides are equal, so its sides are two of 9 m and two of 8 m.
Opposite sides are equal, so the sides are 9, 8, 9, 8: 34 m.

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