Area of a triangle worksheet
Twelve problems in three levels. In the first, students choose which measurements to use: the figures show sides that are not the height, a triangle with the height outside and a rotated one. Then come word problems with units (cm and m, price per square meter) and, at the end, finding the base or the height.
Students check their work with a secret code: each answer has a letter and the letters spell a message. The answers from the most common mistakes (not dividing by 2, using the slanted side) give letters that don't fit.
What's included
- 2 student pages: 12 problems in 3 levels, with figures and a grid to work on.
- Secret code to self-check.
- 1 teacher page: answer key, the mistake behind each wrong answer and an exit question.
Check your answers
The problems
7 cm given? unknownformula
Solve each problem in the grid. Find your answer in the bank (page 2) and write its letter in the box. If all your answers are right, the letters spell a message.
A = b · h2 The height h makes a right angle with the base b.
●○○Level 1 · Using the figure
Every labeled segment is given: choose which ones to use. Figures not to scale.
1
Find the area.
2
Find the area.
3
Find the area.
4
Find the area.
●●○Level 2 · Word problems
5
A triangular garden has a base of 12 m and a height of 8 m. How many m² of grass do you need?
6
A triangular sail has a base of 2.4 m and a height of 3 m. How much fabric does it take?
7
Find the area of a triangle with a base of 50 cm and a height of 1.2 m. Give the answer in m².
8
A triangular parking lot has a base of 40 m and a height of 25 m. Paving costs $30 per m². How much does it cost to pave it?
●●●Level 3 · Working backward
Hint: the rectangle with the same base and height has twice the area, so b · h = 2 · A.
9
A triangle has an area of 750 m² and a height of 50 m. How long is its base?
10
A triangle with an area of 36 cm² has a base of 9 cm. What is its height?
11
What is the height?
12
If you double both the base and the height, what happens to the area? Try it with b = 4 cm and h = 3 cm.
Answer bankno units
Secret code
For the teacher: answer key and common mistakes
Answer key
- 12 × 16 ÷ 2 = 96 cm² (the legs are the base and the height)
- 7 × 5 ÷ 2 = 17.5 cm²
- 4 × 6 ÷ 2 = 12 cm² (the height falls outside the base)
- 9 × 4 ÷ 2 = 18 cm²
- 12 × 8 ÷ 2 = 48 m²
- 2.4 × 3 ÷ 2 = 3.6 m²
- 0.5 × 1.2 ÷ 2 = 0.3 m²
- 40 × 25 ÷ 2 = 500 m²; 500 × 30 = $15,000
- b = 2 × 750 ÷ 50 = 30 m
- h = 2 × 36 ÷ 9 = 8 cm
- h = 2 × 54 ÷ 12 = 9 cm
- 4 × 3 ÷ 2 = 6 → 8 × 6 ÷ 2 = 24: the area is multiplied by 4
The mistake behind each answer in the bank
| Answer | # | Mistake | Answer | # | Mistake |
|---|---|---|---|---|---|
| 192 | 1 | didn't divide by 2 | 30 | 7 | mixed cm and m |
| 48 | 1 | added the three sides (perimeter) | 3,000 | 7 | left the answer in cm² |
| 35 | 2 | didn't divide by 2 | 500 / 30,000 | 8 | stopped at the area / didn't divide by 2 |
| 22.4 | 2 | used the slanted side | 15 / 1,500 | 9 | 750 ÷ 50 without the 2 / didn't divide by the height |
| 13 / 24 | 3 | used the 6.5 cm side / didn't divide by 2 | 4 | 10 | 36 ÷ 9 |
| 36 | 4 | didn't divide by 2 | 4.5 / 108 | 11 | 54 ÷ 12 / didn't divide by the base |
| 96 / 7.2 | 5 / 6 | didn't divide by 2 | × 2 | 12 | thought it doubles |
Mistakes to watch for
- Using the slanted side as the height.
- Forgetting to divide by 2, or working backward with b = A ÷ h (without the 2).
- Mixing units (cm with m, cm with cm²).