Perimeter, area and volume · Ages 10–11

Area of a trapezium 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.What is the area of this trapezium?
Answer:
2.A trapezium's upper base is 3 cm, its lower base 15 cm and its height 12 cm. What is its area in cm²?
Answer:
3.A trapezium's upper base and lower base add up to 21 cm, and its height is 9 cm. What is its area in cm²?
Answer:
4.A trapezium's upper base and lower base add up to 13 cm, and its height is 14 cm. What is its area in cm²?
Answer:
5.A trapezium's upper base is 4 cm, its lower base 20 cm and its height 7 cm. What is its area in cm²?
Answer:

6.Two matching trapeziums, one turned upside down, fit together into a parallelogram. Each trapezium's upper base is 12 cm and its lower base 17 cm. How long is the parallelogram's base?
- A. 29
- B. 34
- C. 204
- D. 17
Choose the right answer
Answer:
7.Two matching trapeziums, one turned upside down, fit together into a parallelogram. Each trapezium's upper base is 9 cm and its lower base 18 cm. How long is the parallelogram's base?
- A. 18
- B. 27
- C. 162
- D. 36
Choose the right answer
Answer:
8.A trapezium has upper base 10 cm, lower base 20 cm, height 6 cm and a slanting side 9 cm. Which working finds its area?
- A. (10 + 20) × 6 ÷ 2
- B. (10 + 20) × 6
- C. 10 × 20 × 6 ÷ 2
- D. (10 + 20) × 9 ÷ 2
Choose the right answer
Answer:
9.A trapezium with upper base 4 cm, lower base 7 cm and height 12 cm has an area of 66 cm².
True or false?
Answer:
10.A trapezium with upper base 6 cm, lower base 9 cm and height 6 cm has an area of 45 cm².
True or false?
Answer:
11.A trapezium has upper base 3 cm, lower base 19 cm, height 8 cm and a slanting side 12 cm. Which working finds its area?
- A. (3 + 19) × 8
- B. (3 + 19) × 12 ÷ 2
- C. (3 + 19) × 8 ÷ 2
- D. 3 × 19 × 8 ÷ 2
Choose the right answer
Answer:
12.A trapezium has upper base 9 cm, lower base 16 cm, height 9 cm and a slanting side 10 cm. Which working finds its area?
- A. (9 + 16) × 10 ÷ 2
- B. 9 × 16 × 9 ÷ 2
- C. (9 + 16) × 9 ÷ 2
- D. (9 + 16) × 9
Choose the right answer
Answer:

13.A handbag's front and back are matching trapeziums, 28 cm along the top, 38 cm along the bottom and 12 cm high. How many cm² of cloth do the two faces take?
Working:
Answer:
14.A trapezium-shaped flowerbed has parallel sides of 5 m and 6 m, 2 m apart. Turf costs $50 a square metre. How many dollars does turfing the whole bed cost?
Working:
Answer:
15.A channel's cross-section is a trapezium: 4 m across at the water's surface, 2 m across the bottom, and 4 m deep. What is the cross-section's area in m²?
Working:
Answer:
16.A trapezium-shaped lawn has parallel sides of 8 m and 26 m, 17 m apart. What is its area in m²?
Working:
Answer:
17.Ka-yee has a rectangle of paper 30 cm by 20 cm and cuts a right-angled triangle off one end: one of its short sides is the rectangle's width, 20 cm, and the other runs 7 cm along its length. What is the area of the trapezium left, in cm²?
Working:
Answer:
18.A handbag's front and back are matching trapeziums, 22 cm along the top, 42 cm along the bottom and 28 cm high. How many cm² of cloth do the two faces take?
Working:
Answer:

Show the answers and working

Area of a trapezium worksheet: Answers and working

1. 24 cm²
Read the upper base 7, lower base 9 and height 3 from the picture. Add the upper and lower bases first.
(upper base + lower base) × height ÷ 2 = (7 + 9) × 3 ÷ 2 = 16 × 3 ÷ 2 = 24.
2. 108 cm²
Use (upper base + lower base) × height ÷ 2. Start with 3 + 15.
(3 + 15) × 12 ÷ 2 = 108 cm².
3. 94.5 cm²
The formula only needs upper base + lower base, which is given: 21. Multiply by the height, and remember to halve.
The formula only needs upper base + lower base: 21 × 9 ÷ 2 = 94.5; you don't need each one.
4. 91 cm²
The formula only needs upper base + lower base, which is given: 13. Multiply by the height, and remember to halve.
The formula only needs upper base + lower base: 13 × 14 ÷ 2 = 91; you don't need each one.
5. 84 cm²
Use (upper base + lower base) × height ÷ 2. Start with 4 + 20.
(4 + 20) × 7 ÷ 2 = 84 cm².

6. A. 29
With the upside-down trapezium beside it, which two lengths make up the parallelogram's base?
The base is the lower base plus the upside-down upper base: 17 + 12 = 29; so the trapezium is 29 × height ÷ 2.
7. B. 27
With the upside-down trapezium beside it, which two lengths make up the parallelogram's base?
The base is the lower base plus the upside-down upper base: 18 + 9 = 27; so the trapezium is 27 × height ÷ 2.
8. A. (10 + 20) × 6 ÷ 2
A trapezium's area needs the upper base, lower base and height. Is the slanting 9 needed? What does the working divide by at the end?
A trapezium's area = (upper base + lower base) × height ÷ 2 = (10 + 20) × 6 ÷ 2.
9. True
Work out (4 + 7) × 12 ÷ 2 yourself, then compare it with 66.
(4 + 7) × 12 ÷ 2 = 66 cm².
10. True
Work out (6 + 9) × 6 ÷ 2 yourself, then compare it with 45.
(6 + 9) × 6 ÷ 2 = 45 cm².
11. C. (3 + 19) × 8 ÷ 2
A trapezium's area needs the upper base, lower base and height. Is the slanting 12 needed? What does the working divide by at the end?
A trapezium's area = (upper base + lower base) × height ÷ 2 = (3 + 19) × 8 ÷ 2.
12. C. (9 + 16) × 9 ÷ 2
A trapezium's area needs the upper base, lower base and height. Is the slanting 10 needed? What does the working divide by at the end?
A trapezium's area = (upper base + lower base) × height ÷ 2 = (9 + 16) × 9 ÷ 2.

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

13. 792 cm²
Find one trapezium face first: (28 + 38) × 12 ÷ 2. How many faces are there?
One face is (28 + 38) × 12 ÷ 2 = 396; two faces are 396 × 2 = 792 cm².
14. 550 dollars
Find the bed's area with (5 + 6) × 2 ÷ 2 first, then multiply by $50 a square metre.
Area (5 + 6) × 2 ÷ 2 = 11 m²; 11 × 50 = $550.
15. 12 m²
The surface and the bottom are the parallel sides, and the depth, 4 m, is the height. Start with 4 + 2.
The surface and the bottom are the parallel sides and the depth is the height: (4 + 2) × 4 ÷ 2 = 12 m².
16. 289 m²
Use (upper base + lower base) × height ÷ 2. Start with 8 + 26.
(8 + 26) × 17 ÷ 2 = 289 m².
17. 530 cm²
You can find the whole sheet, 30 × 20, then take off the triangle cut away, 7 × 20 ÷ 2.
Rectangle 30 × 20 = 600, less the triangle 7 × 20 ÷ 2 = 70: 530. (Or as a trapezium: (30 + 23) × 20 ÷ 2 = 530.)
18. 1792 cm²
Find one trapezium face first: (22 + 42) × 28 ÷ 2. How many faces are there?
One face is (22 + 42) × 28 ÷ 2 = 896; two faces are 896 × 2 = 1792 cm².

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