Free Geometry MCQs with Answers
222 Geometry MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Geometry examines points, lines, angles, triangles, polygons, circles, and three-dimensional figures through properties, theorems, and formulas. Questions connect angle relationships and triangle rules with calculations of perimeter, area, surface area, and volume, so area must not be confused with the space enclosed by a solid.
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222 questions · page 11 of 12
- A. 262 cm2
- B. 384 cm2
- C. 192 cm2
- D. 131 cm2Islamic Studies Quiz
Explanation: The area of a parallelogram is base x perpendicular height. Thus area = 24 cm x 16 cm = 384 cm2.
Correct answer: 384 cm2- A. 225 cm2
- B. 275 cm2
- C. 285 cm2
- D. 315 cm2
Explanation: The area of a trapezium is 1/2 x (sum of parallel sides) x height. Therefore area = 1/2 x (20 cm + 18 cm) x 15 cm = 285 cm2.
Correct answer: 285 cm2- A. 30.48
- B. 29
- C. 34.12
- D. 24
Explanation: The exact conversion is 1 inch = 2.54 cm. Therefore, 12 inches = 12 inches x 2.54 cm per inch = 30.48 cm.
Correct answer: 30.48- A. 2.4 cm
- B. 2.5 cm
- C. 2.54 cm
- D. None
Explanation: The standard exact conversion is 1 inch = 2.54 cm, so the correct value is 2.54 cm.
Correct answer: 2.54 cm- A. Geo means Earth
- B. Metron means Measurement.
- C. Hence Geomatery means
- D. Earth measurement
Explanation: The word geometry comes from the Greek words geo, meaning Earth, and metron, meaning measurement.
Correct answer: Earth measurement- A. (0,1)
- B. (1,1)
- C. (0,0)
- D. (1,0)
Explanation: The origin is the point where the x-axis and y-axis intersect, and both coordinates are zero. Therefore, its coordinates are (0,0).
Correct answer: (0,0)- A. 5 metres
- B. 8 metres
- C. 10 metres
- D. 12 metres
Explanation: Let the horizontal distance be d metres. From the bottom of the pole, tan 60° = 15 metres ÷ d, so d = 5√3 metres; the 30° angle from the…
Correct answer: 10 metres- A. 30°
- B. 45°
- C. 60°
- D. 90°
Explanation: For the right triangle, tan θ = height ÷ shadow length. Since the shadow is √3 times the height, tan θ = height ÷ (√3 x height) = 1/√3…
Correct answer: 30°- A. 149 m
- B. 156 m
- C. 173 m
- D. 200 m
Explanation: Using tan 30° = height/distance, the distance is 100 m ÷ tan 30° = 100 m ÷ 0.577 ≈ 173 m.
Correct answer: 173 m- A. 50°
- B. 60°
- C. 70°
- D. 80°
Explanation: For the right triangle, tan θ = opposite/adjacent = 2√3 m ÷ 2 m = √3, and tan 60° = √3, so θ = 60°.
Correct answer: 60°- A. 173 m
- B. 200 m
- C. 273 m
- D. 300 m
Explanation: The ships are on opposite sides, so their distances from the lighthouse foot are added: 100 m ÷ tan 30° ≈ 173 m and 100 m ÷ tan 45° = 100…
Correct answer: 273 m- A. 2.3 m
- B. 4.6 m
- C. 7.8 m
- D. 9.2 m
Explanation: The 4.6 m distance is adjacent to the 60° angle, so cos 60° = 4.6 m ÷ ladder length; therefore ladder length = 4.6 m ÷ 0.5 = 9.2 m.
Correct answer: 9.2 m- A. 24/5 cm
- B. 12/5 cm
- C. 7/5 cm
- D. None of these
Explanation: AB and AC are each 6 cm, so triangle ABC is isosceles with sides 6 cm, 6 cm and BC.
Correct answer: None of these214. What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
- A. 4:8
- B. 1:4
- C. 6:2
- D. 3:1
Explanation: All squares have the same fixed relationship between side and diagonal, so if one diagonal is three times the other, its side is also…
Correct answer: 3:1- A. 3/2 cm
- B. 1/2 cm
- C. 3/4 cm
- D. 3 cm
Explanation: The altitude of an equilateral triangle is (√3/2) x side. Substituting the side 2√3 cm gives altitude = (√3/2) x 2√3 cm = 3 cm.
Correct answer: 3 cm- A. 4/3 cm
- B. 3/4 cm
- C. 3 cm
- D. 4 cm
Explanation: The area of an equilateral triangle is (√3/4)s². Setting (√3/4)s² = 4√3 cm² gives s² = 16 cm², so s = 4 cm.
Correct answer: 4 cm- A. 20 sq m
- B. 10 sq m
- C. 5 sq m
- D. 3 sq m
Explanation: The triangle area formula is 1/2 x base x height. Substituting base 4 m and height 5 m gives 1/2 x 4 m x 5 m = 10 m².
Correct answer: 10 sq m- A. 0.525cm
- B. 4.2cm
- C. 80%
- D. 60%
Explanation: For similar triangles, areas are proportional to the squares of corresponding heights.
Correct answer: 4.2cm- A. 9cm
- B. 10cm
- C. 11cm
- D. 12cm
Explanation: The ratio sum is 1/2 + 1/3 + 1/4 = 13/12. One ratio unit is therefore 52 cm ÷ (13/12) = 48 cm, and the smallest side is 1/4 × 48 cm = 12…
Correct answer: 12cm- A. 25 cm2
- B. 42 cm2
- C. 49 cm2
- D. None of these
Explanation: For any triangle, area = inradius x semiperimeter. The semiperimeter is 28 cm ÷ 2 = 14 cm, so the area is 2.5 cm x 14 cm = 35 cm2, which…
Correct answer: None of these