Perimeter, area and volume · Ages 10–11

Area of a triangle 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 triangle?
Answer:
2.This is an obtuse triangle; its height is drawn outside it. What is its area?
Answer:
3.A right-angled triangle's two short sides are 3 cm and 4 cm, and its longest side is 5 cm. What is its area in cm²?
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4.A triangle has a base of 21 cm and a height of 8 cm. What is its area in cm²?
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5.A right-angled triangle's two short sides are 12 cm and 16 cm, and its longest side is 20 cm. What is its area in cm²?
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6.A triangle has a base of 24 cm and a height of 6 cm. What is its area in cm²?
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7.Two matching triangles make a parallelogram. Each triangle has base 8 cm and height 9 cm, and the parallelogram's area is 72 cm². What is one triangle's area in cm²?
- A. 36
- B. 72
- C. 18
- D. 144
Choose the right answer
Answer:
8.A triangle with base 13 cm and height 14 cm has an area of 182 cm².
True or false?
Answer:
9.A triangle has its 12 cm side as the base, a height of 11 cm, and another side 12 cm long. Which working finds its area?
- A. 12 × 12 ÷ 2
- B. 12 × 11 ÷ 2
- C. 12 × 11 × 2
- D. 12 × 11
Choose the right answer
Answer:
10.A triangle with base 20 cm and height 5 cm has an area of 50 cm².
True or false?
Answer:
11.A triangle has its 19 cm side as the base, a height of 9 cm, and another side 10 cm long. Which working finds its area?
- A. 19 × 9
- B. 19 × 9 ÷ 2
- C. 19 × 10 ÷ 2
- D. 19 × 9 × 2
Choose the right answer
Answer:
12.A triangle with base 10 cm and height 6 cm has an area of 30 cm².
True or false?
Answer:

13.Ka-yee makes a kite from two triangles that share a 60 cm base; their heights are 29 cm and 28 cm. What is the kite's area in cm²?
Working:
Answer:
14.A triangular sail has a base of 8 m and a height of 8 m. Sailcloth costs $50 a square metre. How many dollars of sailcloth does the sail take?
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15.In a corner of a park, a right-triangular lawn has its two sides along two paths at right angles, 15 m and 20 m long; its third side is 25 m. What is the lawn's area in m²?
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16.A triangular flag has a base of 40 cm and a height of 15 cm. What is its area in cm²?
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17.Tsz-ching cuts a rectangle of paper 19 cm by 12 cm along a diagonal into two triangles. What is the area of each triangle in cm²?
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18.Tsz-ching cuts a rectangle of paper 29 cm by 10 cm along a diagonal into two triangles. What is the area of each triangle in cm²?
Working:
Answer:

Show the answers and working

Area of a triangle worksheet: Answers and working

1. 99 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 = 18 × 11 ÷ 2 = 99.
2. 25 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: 5 × 10 ÷ 2 = 25.
3. 6 cm²
A right-angled triangle's two short sides are square to each other: one is the base, the other the height. Do you need the 5 cm side?
One short side is the base and the other the height: 3 × 4 ÷ 2 = 6; the longest side isn't needed.
4. 84 cm²
A triangle's area is base × height ÷ 2: work out 21 × 8 first, and remember to halve it.
21 × 8 ÷ 2 = 84 cm².
5. 96 cm²
A right-angled triangle's two short sides are square to each other: one is the base, the other the height. Do you need the 20 cm side?
One short side is the base and the other the height: 12 × 16 ÷ 2 = 96; the longest side isn't needed.
6. 72 cm²
A triangle's area is base × height ÷ 2: work out 24 × 6 first, and remember to halve it.
24 × 6 ÷ 2 = 72 cm².

7. A. 36
The parallelogram is made of two triangles of the same size. What part of it is one triangle?
The two triangles are the same size, so one is 72 ÷ 2 = 36.
8. False
Work out 13 × 14 ÷ 2 yourself and compare it with 182. Watch for a missing ÷ 2.
13 × 14 ÷ 2 = 91 cm²: don't forget the ÷ 2.
9. B. 12 × 11 ÷ 2
A triangle's area uses only the base and height. Is the 12 cm side the height? What must the working divide by?
A triangle's area = base × height ÷ 2 = 12 × 11 ÷ 2.
10. True
Work out 20 × 5 ÷ 2 yourself and compare it with 50. Watch for a missing ÷ 2.
20 × 5 ÷ 2 = 50 cm²: don't forget the ÷ 2.
11. B. 19 × 9 ÷ 2
A triangle's area uses only the base and height. Is the 10 cm side the height? What must the working divide by?
A triangle's area = base × height ÷ 2 = 19 × 9 ÷ 2.
12. True
Work out 10 × 6 ÷ 2 yourself and compare it with 30. Watch for a missing ÷ 2.
10 × 6 ÷ 2 = 30 cm²: don't forget the ÷ 2.

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

13. 1710 cm²
Both triangles have base 60. Work them out separately and add, or add the heights first: 29 + 28.
60 × 29 ÷ 2 + 60 × 28 ÷ 2, or in one go 60 × (29 + 28) ÷ 2 = 1710 cm².
14. 1600 dollars
Find the sail's area with base × height ÷ 2 first, then multiply by $50 a square metre.
Area 8 × 8 ÷ 2 = 32 m²; 32 × 50 = $1,600.
15. 150 m²
The two sides along the paths are square to each other: one is the base, the other the height. Is the 25 m side needed?
The two sides at right angles are a base and its height: 15 × 20 ÷ 2 = 150 m²; the 25 m side isn't needed.
16. 300 cm²
A triangle's area is base × height ÷ 2. The base, 40, is even, so halve it first and then multiply by 15.
40 × 15 ÷ 2 = 300 cm² (the base is even, so you can halve it first, then times the height).
17. 114 cm²
Cutting along a diagonal makes two equal triangles. Find the whole sheet's area, 19 × 12, first.
The rectangle 19 × 12 splits into two equal halves: 19 × 12 ÷ 2 = 114 cm².
18. 145 cm²
Cutting along a diagonal makes two equal triangles. Find the whole sheet's area, 29 × 10, first.
The rectangle 29 × 10 splits into two equal halves: 29 × 10 ÷ 2 = 145 cm².

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