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 6 of 12
- A. 14.64cm
- B. 16.36m
- C. 17.60m
- D. 18.40m
Explanation: For a circle, A = pi r², so r² = 24.64 m² ÷ (22/7) = 7.84 m² and r = 2.8 m. Therefore circumference = 2 × 22/7 × 2.8 m = 17.6 m.
Correct answer: 17.60m- A. 110m
- B. 112m
- C. 120cm
- D. 135m
Explanation: For a square, diagonal² = 2 × area, so diagonal² = 2 × 6050 m² = 12100 m². Taking the square root gives a diagonal of 110 m.
Correct answer: 110m- A. 25%
- B. 40.5%
- C. 55%
- D. 56.25%
Explanation: If the original side is s, the new side is 1.25s. Area changes by the square of this factor: (1.25)² = 1.5625, so the increase is 0.5625 ×…
Correct answer: 56.25%104. The area of a rhombus in 2016 Sq.cm and its side is 65cm. The length of its diagonals are________?
- A. 125cm, 35cm
- B. 126cm,32cm
- C. 132cm,26cm
- D. 135cm,25cm
Explanation: The area of a rhombus is half the product of its diagonals, so their product must be 2 × 2016 cm² = 4032 cm².
Correct answer: 126cm,32cm105. The area of largest triangle that can be inscribed in a semicircle of radius R cm is__________?
- A. 2R cm2
- B. R2 cm2
- C. 1/2 R2 cm2
- D. 2 R2 cm2
Explanation: The largest triangle uses the semicircle's diameter as its base, 2R cm, and reaches the arc at height R cm.
Correct answer: R2 cm2- A. No change
- B. 8%decrease
- C. 16% Decrease
- D. 16%increases
Explanation: Triangle area is 1/2 × base × height. The new area factor is 1.40 × 0.60 = 0.84, so the area becomes 84% of its original value and…
Correct answer: 16% Decrease- A. 88cm2
- B. 154cm2
- C. 616cm2
- D. 1250cm2
Explanation: The rectangle's perimeter is 2(18 cm + 26 cm) = 88 cm, so the circle's circumference is also 88 cm.
Correct answer: 616cm2- A. 5:4
- B. 9:4
- C. 4:5
- D. 4:9Fun & Trivia
Explanation: Increasing each side by 50% makes the new side 1.5 times the original side.
Correct answer: 9:4- A. 30m
- B. 40m
- C. 50m
- D. 60m
Explanation: The square has perimeter 160 m, so its side is 160 m ÷ 4 = 40 m and its area is 1600 square metres.
Correct answer: 50m- A. 8cm
- B. 8√2cm
- C. 16cm
- D. 4√2cm
Explanation: For a square, diagonal² = 2 x area. The first diagonal is 4√2 cm, so its area is (4√2 cm)² ÷ 2 = 16 square centimetres.
Correct answer: 8cm- A. 10m
- B. 14.14m
- C. 20m
- D. 25m
Explanation: A square with area 100 square metres has side √100 m = 10 m. The longest straight bamboo that fits inside it is its diagonal, which is…
Correct answer: 14.14m- A. 14m
- B. 18m
- C. 4m
- D. None of these
Explanation: Let the breadth be b metres and the length be 3b metres. Since 3b² = 12 square metres, b² = 4 square metres and b = 2 m, so the length is…
Correct answer: None of these113. The perimeter of a rectangle is 60m. If it's length is twice its breadth then its area is__________?
- A. 160m2
- B. 180m2
- C. 200m2
- D. 220m2
Explanation: Let the breadth be b metres and the length be 2b metres. From 2(l + b) = 60 m, we get 2(3b) = 60 m, so b = 10 m and l = 20 m.
Correct answer: 200m2- A. 295m2
- B. 299m2
- C. 300m2
- D. 375m2
Explanation: The field area is 25 m x 15 m = 375 square metres. The two central passages cover 25 m x 2 m + 15 m x 2 m - 2 m x 2 m = 76 square metres…
Correct answer: 299m2- A. 216
- B. 192
- C. 108
- D. 256
Explanation: Convert the dimensions to centimetres: 12.96 m = 1296 cm and 3.84 m = 384 cm.
Correct answer: 216- A. 485
- B. 431
- C. 391
- D. 381
Explanation: Convert the dimensions to centimetres: 4 m 37 cm = 437 cm and 3 m 23 cm = 323 cm.
Correct answer: 391- A. 56
- B. 42
- C. 38
- D. 34
Explanation: The largest square slab side must divide both floor dimensions exactly.
Correct answer: 34- A. 110
- B. 124
- C. 96
- D. 117
Explanation: Convert the dimensions to centimetres: 6 m 24 cm = 624 cm and 4 m 32 cm = 432 cm.
Correct answer: 117119. If the volume and surface area of a sphere is numerically the same then it's radius is_________?
- A. 1 unit
- B. 2 units
- C. 3 units
- D. 4 units
Explanation: For a sphere, volume is 4/3 x pi x r^3 and surface area is 4 x pi x r^2.
Correct answer: 3 units- A. 3: 5
- B. 2: 5
- C. 3: 1
- D. 1: 3
Explanation: The cylinder volume is pi x r^2 x h_c, while the cone volume is 1/3 x pi x r^2 x h_n.
Correct answer: 1: 3