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 3 of 12
41. If the side of a square is increased by 25 % then how much percent does it's area get increased:
- A. 125
- B. 156.25
- C. 50
- D. 56.25
Explanation: Increasing the side by 25% makes it 1.25 times the original, so the area becomes 1.25² = 1.5625 times the original.
Correct answer: 56.25- A. 260m
- B. 280m
- C. 360m
- D. None of these
Explanation: Let the length and breadth be 5x m and 4x m. Their difference is x m, so x = 20 m; hence the dimensions are 100 m and 80 m, and the…
Correct answer: 360m- A. 50m
- B. 100m
- C. 150m
- D. 200m
Explanation: The total surrounding cost gives the perimeter: 3000 rupees ÷ 7.50 rupees per metre = 400 m.
Correct answer: 50m- A. 37
- B. 38
- C. 39
- D. 40
Explanation: The playground perimeter is 2(36 m + 21 m) = 114 m. At a spacing of 3 m, the number of equal boundary intervals, and therefore flag staffs…
Correct answer: 38- A. 20
- B. 30
- C. 60
- D. None of these
Explanation: The playground is one-third of the plot, so the plot area is 3 × 1200 m² = 3600 m².
Correct answer: None of these46. If the length of diagonal AC of a square ABCD is 5.2 cm then area of the square ABCD is_________?
- A. 15.12 sq.cm
- B. 13.52 sq.cm
- C. 12.62 sq.cm
- D. 10 sq.cm
Explanation: For a square, the diagonal satisfies d² = 2A, so A = d² ÷ 2 = (5.2 cm)² ÷ 2 = 27.04 cm² ÷ 2 = 13.52 cm².
Correct answer: 13.52 sq.cm- A. 160m × 27m
- B. 240m × 18m
- C. 120m × 36m
- D. 135m × 32m
Explanation: Let the smaller side be b m. Three squares first use 3b m of the longer side, and the remaining strip is divided into three squares, so…
Correct answer: 120m × 36m- A. A square with an area of 36 sq.cm
- B. An Equilateral Triangle with a side of 9 cm
- C. A rectangle with 10 cm as length and 40 sq.cm as area
- D. A circle with a radius of 4 cm
Explanation: The square has side √36 cm² = 6 cm, so its perimeter is 24 cm. The triangle perimeter is 3 × 9 cm = 27 cm, the rectangle has breadth 40…
Correct answer: A rectangle with 10 cm as length and 40 sq.cm as area49. The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
- A. 26.4 m2
- B. 39.6 m2
- C. 52.8 m2
- D. 79.2 m2
Explanation: A sector's area is (angle ÷ 360°) × πr². Substituting gives (42° ÷ 360°) × π × (12 m)² = 16.8π m² = 52.8 m² using π = 22/7.
Correct answer: 52.8 m2- A. 0.35 cm2
- B. 17.5 cm2
- C. 8.75 cm2
- D. 55 cm2
Explanation: For a sector, area = 1/2 × radius × arc length. Therefore the area is 1/2 × 5 cm × 3.5 cm = 8.75 cm².
Correct answer: 8.75 cm2- A. (400 - 100π) cm2</sup
- B. (400 - 2π) cm2</sup
- C. (400 - 200π) cm2</sup
- D. 200π cm2</sup
Explanation: Each semicircle has diameter 20 cm, so radius 10 cm; the two semicircles together form one circle of area π(10 cm)² = 100π cm².
Correct answer: (400 - 100π) cm2</sup- A. Rs.45
- B. Rs.78
- C. Rs.44
- D. Rs.40
Explanation: The walk is an annulus with outer radius 15 m and inner radius 13 m, so its area is π[(15 m)² - (13 m)²] = 56π m² = 176 m².
Correct answer: Rs.44- A. 25 cm
- B. 28 cm
- C. 30 cm
- D. 35 cm
Explanation: The perimeter of a semicircle includes its curved part and diameter, so P = πr + 2r.
Correct answer: 28 cm- A. 35.4 cm
- B. 32.4 cm
- C. 32 cm
- D. 30 cm
Explanation: A semicircle's perimeter is πr + 2r, including the diameter. With r = 6.3 cm, P = (22/7 × 6.3 cm) + 12.6 cm = 19.8 cm + 12.6 cm = 32.4 cm.
Correct answer: 32.4 cm- A. 1120 m2
- B. 1250 m2
- C. 1210 m2
- D. 1200 m2
Explanation: The extra grazing area is the annulus formed when the radius increases from 12 m to 23 m: π[(23 m)² - (12 m)²] = 385π m² = 1210 m² using π…
Correct answer: 1210 m256. Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
- A. Rs.150
- B. Rs.132
- C. Rs.100
- D. Rs.125
Explanation: The field's circumference is πd = (22/7) x 28 m = 88 m. Fencing cost = 88 m x Rs.1.50 per m = Rs.132, so option b follows.
Correct answer: Rs.132- A. 124 sq m
- B. 154 sq m
- C. 145 sq m
- D. 167 sq m
Explanation: The area of a circle is πr², so A = (22/7) x 7 m x 7 m = 154 m². Therefore option b is correct.
Correct answer: 154 sq m- A. 20 m
- B. 60 m
- C. 40 m
- D. 80 m
Explanation: The trapezium area is 1/2 x (sum of parallel sides) x depth. Therefore 640 m² = 1/2 x (10 m + 6 m) x depth = 8 m x depth, so depth = 640…
Correct answer: 80 m- A. 8 m
- B. 10 m
- C. 6 m
- D. 12 m
Explanation: Let the base be b m. The altitude is twice the base, so it is 2b m, and the parallelogram area is b x 2b = 2b² = 128 m².
Correct answer: 8 m- A. 260 cm2
- B. 240 cm2
- C. 280 cm2
- D. 220 cm2
Explanation: A rhombus has four equal sides, so each side is 68 cm / 4 = 17 cm. Half of the 16 cm diagonal is 8 cm, and the other half is √(17² - 8²)…
Correct answer: 240 cm2