Right triangles and area
Strand: geometry reasoning
Suggested duration: 30 minutes
Status: New instructional practice, not an official TSIA2 item or score predictor.
Learn — guided worked example
Problem: A right triangle has legs 6 cm and 8 cm. Find its hypotenuse.
- Use the Pythagorean theorem: a² + b² = c².
- Substitute: 6² + 8² = c², so 36 + 64 = 100.
- Take the positive square root: c = 10 cm.
Think about it: Which quantity or operation tells you that the answer is reasonable? Explain in one sentence.
Practice — choose one answer
Work each problem before checking the explanations. The four choices are independent practice, not an official adaptive test.
1. A right triangle has legs 5 and 12. What is its hypotenuse?
- A. 7
- B. 13
- C. 17
- D. 169
2. What is the area of a triangle with base 14 cm and perpendicular height 5 cm?
- A. 19 cm²
- B. 35 cm²
- C. 70 cm²
- D. 140 cm²
3. A rectangle measures 7 m by 9 m. What is its perimeter?
- A. 16 m
- B. 32 m
- C. 63 m
- D. 126 m
4. A right triangle has hypotenuse 10 and one leg 8. What is the other leg?
- A. 2
- B. 4
- C. 6
- D. 18
Reflect
Which step was most difficult? Write a correction in your own words, then solve a similar problem without looking at the worked example.