NJSLA Geometric Principles and Measurement 3 — Questions and Answers
Question 1: On a coordinate plane, point A is at (2, 3) and point B is at (8, 11). What is the length of segment AB?
- 8
- 10 (Correct answer)
- 12
- 14
Correct answer: 10
Distance = √((8−2)² + (11−3)²) = √(36 + 64) = √100 = 10.
Question 2: A regular hexagon has a side length of 6 cm. How many lines of symmetry does it have?
- 3
- 4
- 6 (Correct answer)
- 8
Correct answer: 6
A regular hexagon has 6 lines of symmetry — three through opposite vertices and three through midpoints of opposite sides.
Question 3: What is the surface area of a cube with edge length 5 cm?
- 25 cm²
- 100 cm²
- 125 cm²
- 150 cm² (Correct answer)
Correct answer: 150 cm²
A cube has 6 faces, each with area 5² = 25 cm², so total surface area = 6 × 25 = 150 cm².
Question 4: Triangle ABC is similar to triangle DEF. If AB = 6, BC = 9, and DE = 10, what is EF?
- 12
- 15 (Correct answer)
- 18
- 20
Correct answer: 15
The scale factor is DE/AB = 10/6 = 5/3, so EF = BC × (5/3) = 9 × 5/3 = 15.
Question 5: A circle has a circumference of 31.4 cm. What is its area? (Use π ≈ 3.14)
- 78.5 cm² (Correct answer)
- 50 cm²
- 25 cm²
- 100 cm²
Correct answer: 78.5 cm²
C = 2πr → r = 31.4/(2 × 3.14) = 5 cm; Area = πr² = 3.14 × 25 = 78.5 cm².
Question 6: Which of the following sets of side lengths forms a valid triangle?
- 2, 3, 7
- 4, 5, 10
- 6, 8, 15
- 5, 7, 11 (Correct answer)
Correct answer: 5, 7, 11
The Triangle Inequality requires the sum of any two sides to exceed the third; 5 + 7 = 12 > 11, so this set is valid.
Question 7: A trapezoid has parallel bases of 8 m and 14 m, and a height of 6 m. What is its area?
- 66 m² (Correct answer)
- 72 m²
- 84 m²
- 132 m²
Correct answer: 66 m²
Area of trapezoid = ½ × (b₁ + b₂) × h = ½ × (8 + 14) × 6 = ½ × 22 × 6 = 66 m².
NJSLA Geometric Principles and Measurement 3
On a coordinate plane, point A is at (2, 3) and point B is at (8, 11).
What is the length of segment AB?