West B Test Math: Geometry and Measurement 4 — Questions and Answers
Question 1: A rectangular prism has a length of 8 ft, width of 3 ft, and height of 5 ft. What is its surface area?
- 120 ft²
- 158 ft² (Correct answer)
- 158 ft²
- 190 ft²
Correct answer: 158 ft²
Surface area = 2(lw + lh + wh) = 2(24 + 40 + 15) = 2(79) = 158 ft².
Question 2: On a coordinate plane, what is the distance between points (1, 2) and (4, 6)?
- 3 units
- 4 units
- 5 units (Correct answer)
- 7 units
Correct answer: 5 units
Distance = √((4−1)² + (6−2)²) = √(9 + 16) = √25 = 5 units.
Question 3: A sector of a circle has a central angle of 90° and a radius of 6 cm. What is the area of the sector? (Use π ≈ 3.14)
- 9.42 cm²
- 18.84 cm²
- 28.26 cm² (Correct answer)
- 56.52 cm²
Correct answer: 28.26 cm²
Area = (90/360) × π × 6² = 0.25 × 3.14 × 36 = 28.26 cm².
Question 4: Which of the following is NOT a property of a parallelogram?
- Opposite sides are parallel
- Opposite angles are equal
- All angles are 90° (Correct answer)
- Diagonals bisect each other
Correct answer: All angles are 90°
A parallelogram does not require right angles; rectangles and squares are special parallelograms that have 90° angles.
Question 5: If a polygon has an interior angle sum of 1080°, how many sides does it have?
- 6
- 7
- 8 (Correct answer)
- 9
Correct answer: 8
Using (n−2) × 180° = 1080°, we get n−2 = 6, so n = 8 sides.
Question 6: A room's floor is 12 feet by 15 feet. How many square yards of carpet are needed to cover it?
- 180 sq yd
- 60 sq yd
- 20 sq yd (Correct answer)
- 27 sq yd
Correct answer: 20 sq yd
Area = 12 × 15 = 180 sq ft; converting: 180 ÷ 9 = 20 sq yd (since 1 sq yd = 9 sq ft).
Question 7: Two similar triangles have corresponding sides in the ratio 3:5. If the smaller triangle has an area of 27 cm², what is the area of the larger triangle?
- 45 cm²
- 50 cm²
- 75 cm² (Correct answer)
- 135 cm²
Correct answer: 75 cm²
Area ratio = (3:5)² = 9:25; larger area = 27 × (25/9) = 75 cm².
West B Test Math: Geometry and Measurement 4
A rectangular prism has a length of 8 ft, width of 3 ft, and height of 5 ft.
What is its surface area?