CAHSEE Measurement and Geometry 5 — Questions and Answers
Question 1: The length of a rectangle is three times its width. If the perimeter is 48 inches, what is the width?
- 6 inches (Correct answer)
- 12 inches
- 8 inches
- 4 inches
Correct answer: 6 inches
Let width = w; then 2(w + 3w) = 48 → 8w = 48 → w = 6 inches.
Question 2: A circle has an area of 78.5 cm². What is its radius? (Use π ≈ 3.14)
- 5 cm (Correct answer)
- 25 cm
- 10 cm
- 12.5 cm
Correct answer: 5 cm
Area = πr² → 78.5 = 3.14r² → r² = 25 → r = 5 cm.
Question 3: Triangle ABC has angles A = 45° and B = 75°. What is the measure of angle C?
- 80°
- 120°
- 60° (Correct answer)
- 90°
Correct answer: 60°
The sum of angles in a triangle is 180°; C = 180° − 45° − 75° = 60°.
Question 4: A figure is reflected across the y-axis. If a vertex was originally at (3, −2), where is the new vertex?
- (−3, 2)
- (−3, −2) (Correct answer)
- (3, 2)
- (−2, 3)
Correct answer: (−3, −2)
Reflecting across the y-axis negates the x-coordinate: (3, −2) → (−3, −2).
Question 5: A square pyramid has a square base with side length 6 m and a height of 8 m. What is its volume?
- 288 m³
- 144 m³
- 96 m³ (Correct answer)
- 192 m³
Correct answer: 96 m³
Volume = (1/3) × base area × height = (1/3) × 36 × 8 = 96 m³.
Question 6: Two parallel lines are cut by a transversal. One alternate interior angle measures 72°. What is the measure of the other alternate interior angle?
- 108°
- 18°
- 72° (Correct answer)
- 144°
Correct answer: 72°
Alternate interior angles are congruent when formed by parallel lines and a transversal, so the angle is also 72°.
Question 7: Which formula gives the surface area of a rectangular prism with length l, width w, and height h?
- l × w × h
- 2lw + 2lh + 2wh (Correct answer)
- lw + lh + wh
- 2(l + w + h)
Correct answer: 2lw + 2lh + 2wh
Surface area = 2lw + 2lh + 2wh accounts for all six rectangular faces of the prism.
CAHSEE Measurement and Geometry 5
The length of a rectangle is three times its width.
If the perimeter is 48 inches, what is the width?