Perimeter, area and volume · Ages 10–11

From an area back to a base or height worksheet

Part of: Areas of parallelograms, triangles and trapeziums

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Perimeter, area and volume · Ages 10–11

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

1.The triangle's area is 50 cm². How many centimetres is its height?
Answer:
2.The parallelogram's area is 128 cm². How many centimetres is its base?
Answer:
3.The triangle's area is 39 cm². How many centimetres is its height?
Answer:
4.The parallelogram's area is 112 cm². How many centimetres is its base?
Answer:
5.The trapezium's area is 75 cm². How many centimetres is its upper base?
Answer:
6.The trapezium's area is 144 cm². How many centimetres is its height?
Answer:
7.The trapezium's area is 133 cm². How many centimetres is its upper base?
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8.The trapezium's area is 119 cm². How many centimetres is its height?
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9.A triangle has base 14 cm and height 11 cm. What part of a parallelogram with the same base and height is its area?
- A. Twice
- B. A quarter
- C. The same
- D. Half
Choose the right answer
Answer:
10.A triangle has base 17 cm and height 9 cm. What part of a parallelogram with the same base and height is its area?
- A. Twice
- B. A quarter
- C. The same
- D. Half
Choose the right answer
Answer:
11.A triangle's area is 78 cm² and its base 13 cm, so its height is 12 cm.
True or false?
Answer:
12.A triangle's area is 70 cm² and its base 10 cm, so its height is 14 cm.
True or false?
Answer:

13.A trapezium-shaped field has an area of 330 m², with parallel sides 7 m and 37 m. How many metres is its height?
Working:
Answer:
14.A triangular flowerbed has an area of 30 m² and a base of 6 m. How many metres is its height?
Working:
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15.A parallelogram parking space has an area of 12 m² and a height of 4 m. How many metres is its base?
Working:
Answer:
16.Ka-lok cuts out a rectangle 10 cm by 9 cm, then a triangle with the same area and a base of 18 cm. How many centimetres is the triangle's height?
Working:
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17.Ming cuts out a rectangle 15 cm by 9 cm, then a triangle with the same area and a base of 18 cm. How many centimetres is the triangle's height?
Working:
Answer:
18.A parallelogram parking space has an area of 20 m² and a height of 5 m. How many metres is its base?
Working:
Answer:

Show the answers and working

From an area back to a base or height worksheet: Answers and working

1. 10 cm
Area = base × height ÷ 2, so work backwards: double 50 first, then think what to divide by.
Height = area × 2 ÷ base = 50 × 2 ÷ 10 = 10.
2. 16 cm
Area = base × height, so base = area ÷ height. Find the height in the picture.
Base = area ÷ height = 128 ÷ 8 = 16.
3. 13 cm
Area = base × height ÷ 2, so work backwards: double 39 first, then think what to divide by.
Height = area × 2 ÷ base = 39 × 2 ÷ 6 = 13.
4. 8 cm
Area = base × height, so base = area ÷ height. Find the height in the picture.
Base = area ÷ height = 112 ÷ 14 = 8.
5. 3 cm
First find upper base + lower base from the area: 75 × 2 ÷ 10.
With the two sides' total, subtract the lower base, 12.
Upper base + lower base = 75 × 2 ÷ 10 = 15; upper base = 15 − 12 = 3.
6. 12 cm
First add the upper and lower bases, then double 144 and divide by that sum.
Height = area × 2 ÷ (upper base + lower base) = 144 × 2 ÷ 24 = 12.
7. 5 cm
First find upper base + lower base from the area: 133 × 2 ÷ 14.
With the two sides' total, subtract the lower base, 14.
Upper base + lower base = 133 × 2 ÷ 14 = 19; upper base = 19 − 14 = 5.
8. 7 cm
First add the upper and lower bases, then double 119 and divide by that sum.
Height = area × 2 ÷ (upper base + lower base) = 119 × 2 ÷ 34 = 7.

9. D. Half
Compare the formulas: the triangle is 14 × 11 ÷ 2, the parallelogram 14 × 11.
Triangle 14 × 11 ÷ 2, parallelogram 14 × 11: the triangle is half.
10. D. Half
Compare the formulas: the triangle is 17 × 9 ÷ 2, the parallelogram 17 × 9.
Triangle 17 × 9 ÷ 2, parallelogram 17 × 9: the triangle is half.
11. True
A triangle's height = area × 2 ÷ base. Work out 78 × 2 ÷ 13, then compare it with 12.
A triangle's height = area × 2 ÷ base = 78 × 2 ÷ 13 = 12.
12. True
A triangle's height = area × 2 ÷ base. Work out 70 × 2 ÷ 10, then compare it with 14.
A triangle's height = area × 2 ÷ base = 70 × 2 ÷ 10 = 14.

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

13. 15 m
Area = (upper base + lower base) × height ÷ 2. Add 7 + 37, and double 330.
Height = 330 × 2 ÷ (7 + 37) = 330 × 2 ÷ 44 = 15 m.
14. 10 m
Area = base × height ÷ 2. Work backwards: double 30, then divide by the base, 6.
Height = 30 × 2 ÷ 6 = 10 m.
15. 3 m
Area = base × height, so base = area ÷ height. Work out 12 ÷ 4.
Base = 12 ÷ 4 = 3 m.
16. 10 cm
Find the rectangle's area, 10 × 9, first; the triangle has the same area.
A triangle's height = area × 2 ÷ base, and the base is 18.
Area = 10 × 9 = 90; the triangle's height = 90 × 2 ÷ 18 = 10 cm.
17. 15 cm
Find the rectangle's area, 15 × 9, first; the triangle has the same area.
A triangle's height = area × 2 ÷ base, and the base is 18.
Area = 15 × 9 = 135; the triangle's height = 135 × 2 ÷ 18 = 15 cm.
18. 4 m
Area = base × height, so base = area ÷ height. Work out 20 ÷ 5.
Base = 20 ÷ 5 = 4 m.

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