Perimeter, area and volume · Ages 10–11
Areas of parallelograms, triangles and trapeziums worksheet
Covers: Heights of triangles and quadrilaterals, Area of a parallelogram, Area of a triangle, Area of a trapezium, Areas of triangles, parallelograms and trapeziums together, From an area back to a base or height, Areas of polygons
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Areas of parallelograms, triangles and trapeziums worksheet
Perimeter, area and volume · Ages 10–11
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A parallelogram has a base of 10 cm and a height of 11 cm. What is its area in cm²?
Answer:
2.What is the area of this triangle?
Answer:
3.This is an obtuse triangle; its height is drawn outside it. What is its area?
Answer:
4.A trapezium's upper base and lower base add up to 15 cm, and its height is 6 cm. What is its area in cm²?
Answer:
5.Area of the parallelogram = ? cm²
Answer:
6.Area of the parallelogram = ? cm²
Answer:
7.The trapezium's area is 40 cm². How many centimetres is its upper base?
Answer:
8.What is the area of the polygon in the picture?
Answer:
Part B: Choose, or true or false (2 marks each)
9.In which picture is the dashed line the trapezium's height for the thick base?
- A
- B
- C
- D
Choose the right picture
Answer:
10.In which picture is the dashed line the parallelogram's height for the thick base?
- A
- B
- C
- D
Choose the right picture
Answer:
11.A parallelogram has base 20 cm, height 7 cm and slanting sides 10 cm. Cut the triangle off one end along the height and move it to the other end to make a rectangle. How long and how wide is the rectangle?
- A. 20 cm long, 10 cm wide
- B. 20 cm long, 7 cm wide
- C. 10 cm long, 7 cm wide
- D. 40 cm long, 7 cm wide
Choose the right answer
Answer:
12.Two matching trapeziums, one turned upside down, fit together into a parallelogram. Each trapezium's upper base is 5 cm and its lower base 9 cm. How long is the parallelogram's base?
- A. 45
- B. 18
- C. 14
- D. 9
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.Tsz-ching measures a triangle: with its 11 cm side as the base, the height is 12 cm. With another side, 12 cm, as the base, what is the height?
Working:
Answer:
14.A parallelogram-shaped tile has a base of 20 cm and a height of 15 cm. How many of these tiles exactly cover an area of 13200 cm²?
Working:
Answer:
15.Tsz-ching makes a kite from two triangles that share a 36 cm base; their heights are 11 cm and 20 cm. What is the kite's area in cm²?
Working:
Answer:
16.A triangular lawn has a base of 29 m and a height of 8 m. What is its area, in square metres?
Working:
Answer:
17.A parallelogram parking space has an area of 45 m² and a height of 9 m. How many metres is its base?
Working:
Answer:
18.The picture is the plan of an L-shaped living room. Flooring costs $80 a square metre. How many dollars does flooring the whole room cost?
Working:
Answer:
Show the answers and working
Areas of parallelograms, triangles and trapeziums worksheet: Answers and working
Part A: Working out and filling in
1. 110 cm²
A parallelogram's area is base × height: multiply 10 by 11.
10 × 11 = 110 cm².
2. 78 cm²
Find the base and height in the picture and use base × height ÷ 2. Halving the even one first makes it easier.
Area = base × height ÷ 2 = 13 × 12 ÷ 2 = 78.
3. 72 cm²
A height outside works just the same: the base is the thick side, the height the dashed line. Use base × height ÷ 2.
A height outside is still base × height ÷ 2: 16 × 9 ÷ 2 = 72.
4. 45 cm²
The formula only needs upper base + lower base, which is given: 15. Multiply by the height, and remember to halve.
The formula only needs upper base + lower base: 15 × 6 ÷ 2 = 45; you don't need each one.
5. Area of the parallelogram = 56 cm²
A parallelogram's area is base × height: 8 × 7 = 56, so 56 cm²
6. Area of the parallelogram = 96 cm²
A parallelogram's area is base × height (the slanting 13 cm side is not the height): 8 × 12 = 96, so 96 cm²
7. 2 cm
First find upper base + lower base from the area: 40 × 2 ÷ 5.
With the two sides' total, subtract the lower base, 14.
Upper base + lower base = 40 × 2 ÷ 5 = 16; upper base = 16 − 14 = 2.
8. 292 cm²
Fill in the notch to make a 20 × 16 rectangle. Work that out, then take off the 4 × 7 notch.
Fill in to a 20 × 16 rectangle and take off the 4 × 7 notch: 292.
Part B: Choose, or true or false
9. B
Where are the trapezium's two parallel sides? Look for a dashed line joining them that is square to the thick side.
A trapezium's height is the square line between its two parallel sides.
10. C
The thick side is the base. Look for a dashed line that drops square from the opposite side to it.
A parallelogram's height runs square from the side opposite the base down to the base.
11. B. 20 cm long, 7 cm wide
After the move, which sides of the rectangle do the old base and height become? Is the slanting 10 still on the edge?
After the move it is the base 20 long and the height 7 wide, with the same area: 20 × 7.
12. C. 14
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: 9 + 5 = 14; so the trapezium is 14 × height ÷ 2.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 11 cm
Same triangle, same area whichever base you use. Work out 11 × 12, then ask what 12 times that height must give it.
Same triangle, same area: 11 × 12 ÷ 2 = 12 × height ÷ 2, so height = 11 × 12 ÷ 12 = 11 cm.
14. 44 tiles
Find one tile's area, 20 × 15, first, then see how many of those fit in 13200.
One tile is 20 × 15 = 300 cm²; 13200 ÷ 300 = 44 tiles.
15. 558 cm²
Both triangles have base 36. Work them out separately and add, or add the heights first: 11 + 20.
36 × 11 ÷ 2 + 36 × 20 ÷ 2, or in one go 36 × (11 + 20) ÷ 2 = 558 cm².
16. A triangular lawn has a base of 29 m and a height of 8 m. What is its area, in square metres? (Answer: 116 m²)
29 × 8 ÷ 2 = 116
17. 5 m
Area = base × height, so base = area ÷ height. Work out 45 ÷ 9.
Base = 45 ÷ 9 = 5 m.
18. 7120 dollars
Fill in the missing corner and the room is a 13 × 8 rectangle. Take off the corner for the area, then multiply by $80.
The missing corner is 13 − 10 = 3 m by 8 − 3 = 5 m. Area = 13 × 8 − 3 × 5 = 89 m², and 89 × 80 = $7,120.
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