Perimeter, area and volume · Ages 10–11

Heights of triangles and quadrilaterals worksheet

Part of: Areas of parallelograms, triangles and trapeziums

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Perimeter, area and volume · Ages 10–11

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

1.In which picture is the dashed line the triangle's height for the thick base?
- A
- B
- C
- D
Choose the right picture
Answer:
2.What angle does a triangle's height make with its base?
- A. It depends on the triangle
- B. An acute angle
- C. An obtuse angle
- D. A right angle
Choose the right answer
Answer:
3.The dashed line is the triangle's height for the thick base.
True or false?
Answer:
4.In which picture is the dashed line the parallelogram's height for the thick base?
- A
- B
- C
- D
Choose the right picture
Answer:
5.In which picture is the dashed line the trapezium's height for the thick base?
- A
- B
- C
- D
Choose the right picture
Answer:

6.A parallelogram plot has height 5 m when its 8 m side is the base. What is its height when its other side, 10 m, is the base?
Working:
Answer:
7.May wants to measure a triangular board's height for the thick base. Which picture's dashed line should May measure?
- A
- B
- C
- D
Choose the right picture
Working:
Answer:
8.Ming measures a triangle: with its 6 cm side as the base, the height is 13 cm. With another side, 13 cm, as the base, what is the height?
Working:
Answer:
9.Ka-yee wants to measure a triangular board's height for the thick base. Which picture's dashed line should Ka-yee measure?
- A
- B
- C
- D
Choose the right picture
Working:
Answer:
10.Tsz-ching measures a triangle: with its 14 cm side as the base, the height is 5 cm. With another side, 7 cm, as the base, what is the height?
Working:
Answer:
11.Ka-yee measures a triangle: with its 10 cm side as the base, the height is 13 cm. With another side, 13 cm, as the base, what is the height?
Working:
Answer:

Show the answers and working

Heights of triangles and quadrilaterals worksheet: Answers and working

1. D
In each picture, check the dashed line: is it square to the thick side, and does it reach the opposite corner?
A height is square to the thick base and runs from it to the opposite corner.
2. D. A right angle
Think how a height is drawn: with a set square, square from the corner to the base.
A height runs from the corner square to the base (or the base carried on), so it always makes a right angle with the base.
3. False
First check the dashed line is square to the thick side, then that it runs from it to the opposite corner.
Check two things: square to the thick side, and reaching from it to the opposite corner.
4. B
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.
5. C
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.

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

6. 4 m
Changing the base doesn't change the area. Work out the area, 8 × 5, then think what to divide by.
The area stays the same: 8 × 5 = 10 × height, so height = 8 × 5 ÷ 10 = 4 m.
7. D
The line May measures must be square to the thick side and reach the opposite corner. Check both in each picture.
A height is the square distance from the base to the opposite corner.
8. 6 cm
Same triangle, same area whichever base you use. Work out 6 × 13, then ask what 13 times that height must give it.
Same triangle, same area: 6 × 13 ÷ 2 = 13 × height ÷ 2, so height = 6 × 13 ÷ 13 = 6 cm.
9. C
The line Ka-yee measures must be square to the thick side and reach the opposite corner. Check both in each picture.
A height is the square distance from the base to the opposite corner.
10. 10 cm
Same triangle, same area whichever base you use. Work out 14 × 5, then ask what 7 times that height must give it.
Same triangle, same area: 14 × 5 ÷ 2 = 7 × height ÷ 2, so height = 14 × 5 ÷ 7 = 10 cm.
11. 10 cm
Same triangle, same area whichever base you use. Work out 10 × 13, then ask what 13 times that height must give it.
Same triangle, same area: 10 × 13 ÷ 2 = 13 × height ÷ 2, so height = 10 × 13 ÷ 13 = 10 cm.

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