Build geometry problem-solving skills with comprehensive practice questions on shapes, angles, area, volume, coordinate geometry, and geometric proofs. Each question includes detailed explanations, geometric reasoning, and formula applications. Perfect for high school geometry, honors geometry, or SAT/ACT Math Level 2 prep.
12 sample questions. Expand to see answers and explanations.
1. What is the sum of interior angles in a hexagon?
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Answer
720°
Explanation
Formula: (n-2) × 180° where n = number of sides. Hexagon has 6 sides: (6-2) × 180° = 4 × 180° = 720°. This formula works for ANY polygon.
Type: multiple choice
2. A right triangle has legs 6 and 8. Find the hypotenuse.
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Answer
10
Explanation
Pythagorean theorem: a² + b² = c². So 6² + 8² = c², 36 + 64 = 100, c = √100 = 10. This is a Pythagorean triple (3-4-5 scaled by 2).
Type: multiple choice
3. What is the volume of a cylinder with radius 3 and height 5?
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Answer
45π (approximately 141.37)
Explanation
V = πr²h = π(3)²(5) = π(9)(5) = 45π ≈ 141.37 cubic units. Remember: volume is in cubic units, area in square units.
Type: multiple choice
4. Two parallel lines cut by a transversal. One angle is 65°. What is the corresponding angle?
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Answer
65°
Explanation
Corresponding angles are equal when parallel lines are cut by a transversal. Also: alternate interior angles are equal, co-interior angles sum to 180°.
Type: multiple choice
5. A triangle has sides 5, 12, and 13. Is it a right triangle?
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Answer
Yes
Explanation
Check if a² + b² = c² (Pythagorean theorem). 5² + 12² = 25 + 144 = 169 = 13². Yes, it's a right triangle. Another Pythagorean triple.
Type: true false
6. What is the area of a trapezoid with bases 8 and 12 and height 5?
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Answer
50
Explanation
A = ½(b₁ + b₂)h = ½(8 + 12)(5) = ½(20)(5) = 50 square units. Average the bases, multiply by height.
Type: multiple choice
7. A regular octagon has one interior angle measuring:
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Answer
135°
Explanation
Each interior angle = (n-2)×180°/n. For octagon (n=8): (8-2)×180°/8 = 1080°/8 = 135°. Regular means all angles equal.
Type: multiple choice
8. Distance between points (2,3) and (5,7) in coordinate plane?
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Answer
5
Explanation
Distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²] = √[(5-2)² + (7-3)²] = √[9 + 16] = √25 = 5. Pythagorean theorem in coordinates.
Type: multiple choice
9. True or False: The diagonals of a rectangle bisect each other.
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Answer
True
Explanation
True. Rectangle diagonals bisect each other AND are equal in length. But they do NOT intersect at right angles (that's rhombus/square).
Type: true false
10. Surface area of a sphere with radius 3?
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Answer
36π (approximately 113.10)
Explanation
SA = 4πr² = 4π(3)² = 4π(9) = 36π ≈ 113.10 square units. Volume would be (4/3)πr³.
Type: multiple choice
11. If two triangles have sides in ratio 2:3, their areas are in ratio:
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Answer
4:9
Explanation
When linear dimensions scale by k, area scales by k². Here k = 3/2, so area ratio = (3/2)² = 9/4 = 4:9. Volume scales by k³.
Type: multiple choice
12. Exterior angle of triangle equals 110°. What is sum of non-adjacent interior angles?
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Answer
110°
Explanation
Exterior angle theorem: exterior angle equals sum of two non-adjacent interior angles. So sum = 110°. Classic geometry theorem.
Type: multiple choice
Workflow
Take practice test to find challenging problem types—don't look at answers first
Review geometric principles and formulas for missed concepts
Practice drawing accurate diagrams—label all given information
Work through explanations step-by-step to understand reasoning
Retake test after focused study to measure growth
Tips
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Generate Now — FreeShapes, angles, area, volume, Pythagorean theorem, similar figures, coordinate geometry, parallel lines, polygon angles, surface area, transformations, and geometric reasoning.
Questions focus on calculations and conceptual understanding. For formal two-column or paragraph proofs, pair these practice problems with your textbook's proof exercises.
Master formulas first (area, volume, distance). Then practice problem types (angles, triangles, circles). Finally, work full practice tests under timed conditions.
Area is 2D measurement (square units)—surface of flat shapes. Volume is 3D measurement (cubic units)—space inside solid figures.