GAT Geometry and Spatial 2 — Questions and Answers
Question 1: How many lines of symmetry does a regular hexagon have?
- 3
- 4
- 6 (Correct answer)
- 12
Correct answer: 6
A regular hexagon has 6 lines of symmetry: 3 through opposite vertices and 3 through the midpoints of opposite sides. The number of symmetry lines equals the number of sides for regular polygons.
Question 2: A right triangle has legs of length 6 cm and 8 cm. What is the length of the hypotenuse?
- 7 cm
- 10 cm (Correct answer)
- 12 cm
- 14 cm
Correct answer: 10 cm
By the Pythagorean theorem: c² = a² + b² = 6² + 8² = 36 + 64 = 100. c = √100 = 10 cm. This is a 3-4-5 right triangle scaled by 2.
Question 3: What is the sum of interior angles of a pentagon?
- 360°
- 480°
- 540° (Correct answer)
- 720°
Correct answer: 540°
Sum of interior angles = (n-2) × 180° = (5-2) × 180° = 3 × 180° = 540°. This formula works for any polygon.
Question 4: If you fold a flat cross shape (6 squares arranged in a plus sign), what 3D shape do you get?
- Pyramid
- Cube (Correct answer)
- Cylinder
- Triangular prism
Correct answer: Cube
A cross-shaped net (one center square with four squares on each side plus one on the end) folds into a cube. Each square becomes one face of the cube. Spatial visualization is tested on the Qudurat.
Question 5: Two parallel lines are cut by a transversal. One alternate interior angle measures 55°. What does the other alternate interior angle measure?
- 35°
- 55° (Correct answer)
- 125°
- 180°
Correct answer: 55°
Alternate interior angles formed by a transversal cutting parallel lines are always equal. Therefore, the other alternate interior angle is also 55°.
Question 6: A sector of a circle has a central angle of 90° and radius 8 cm. What is its area?
- 16π cm² (Correct answer)
- 32π cm²
- 64π cm²
- 8π cm²
Correct answer: 16π cm²
Sector area = (θ/360°) × πr² = (90/360) × π × 8² = (1/4) × 64π = 16π cm² ≈ 50.27 cm².
GAT Geometry and Spatial 2
How many lines of symmetry does a regular hexagon have?