CAHSEE Measurement and Geometry 3 — Questions and Answers
Question 1: A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
- 10 (Correct answer)
- 14
- 7
- 100
Correct answer: 10
Using the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100, so c = 10.
Question 2: A scale drawing uses a scale of 1 inch = 20 feet. If a hallway is 3.5 inches long on the drawing, how long is the actual hallway?
- 23.5 feet
- 70 feet (Correct answer)
- 57 feet
- 35 feet
Correct answer: 70 feet
Actual length = 3.5 × 20 = 70 feet.
Question 3: Which of the following correctly describes supplementary angles?
- Two angles that sum to 90°
- Two angles that are equal
- Two angles that sum to 180° (Correct answer)
- Two angles that sum to 360°
Correct answer: Two angles that sum to 180°
Supplementary angles are two angles whose measures add up to 180°.
Question 4: A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
- 188.4 cm³
- 282.6 cm³ (Correct answer)
- 94.2 cm³
- 942 cm³
Correct answer: 282.6 cm³
Volume = π × r² × h = 3.14 × 9 × 10 = 282.6 cm³.
Question 5: Triangle PQR is similar to triangle STU. The sides of PQR are 3, 4, and 5. If the shortest side of STU is 9, what is the longest side of STU?
- 12
- 15 (Correct answer)
- 18
- 27
Correct answer: 15
The scale factor is 9 ÷ 3 = 3, so the longest side is 5 × 3 = 15.
Question 6: A rectangular garden is 12 feet wide and has an area of 180 square feet. What is its length?
- 168 feet
- 15 feet (Correct answer)
- 18 feet
- 12 feet
Correct answer: 15 feet
Area = length × width, so length = 180 ÷ 12 = 15 feet.
Question 7: Which transformation moves every point of a figure the same distance in the same direction without rotating or flipping it?
- Reflection
- Rotation
- Translation (Correct answer)
- Dilation
Correct answer: Translation
A translation slides a figure without changing its size, shape, or orientation.
CAHSEE Measurement and Geometry 3
A right triangle has legs of length 6 and 8.
What is the length of the hypotenuse?