Free Area and Volume MCQs with Answers

• A. 529 sq m
• B. 240 sq m
• C. 260 sq m
• D. 480 sq m

Explanation: The diagonals of a rhombus bisect each other at right angles. Half of the known diagonal is 10 m, so the other half is √(26² - 10²) m =…

• A. Rs.3600
• B. Rs.3700
• C. Rs.3800
• D. Rs.3900

Explanation: The road parallel to the length covers 80 m x 10 m = 800 m², and the road parallel to the breadth covers 60 m x 10 m = 600 m².

• A. 675, Rs.1350
• B. 575, Rs.1350
• C. 1350, Rs.675
• D. None

Explanation: A 2.5 m path outside increases each dimension by 5 m, giving outer dimensions 80 m x 60 m.

• A. 432 sq m
• B. 356 sq m
• C. 452 sq m
• D. 428 sq m

Explanation: Let the breadth be b m, so the length is 3b m. From the perimeter, 2(3b + b) = 96 m, giving 8b = 96 m and b = 12 m; length = 36 m.

• A. Rs.1014
• B. Rs.1140
• C. Rs.999
• D. Rs.1085

Explanation: The square's side is √3136 m = 56 m, so its perimeter is 4 x 56 m = 224 m.

• A. Rs.700
• B. Rs.1200
• C. Rs.1400
• D. Rs.1500

Explanation: The long side is 1200 m² / 30 m = 40 m. The diagonal is √(30² + 40²) m = 50 m, so the fenced length is 40 m + 30 m + 50 m = 120 m and the…

• A. 31 m
• B. 32 m
• C. 16 m
• D. 20 m

Explanation: The square pond has area 8 m x 8 m = 64 m². Since this is 1/8 of the field, field area = 8 x 64 m² = 512 m²; with length twice width, 2w²…

• A. 425
• B. 476
• C. 450
• D. 350

Explanation: Leaving a 0.25 m border on every side leaves a floor area of (4 m - 0.5 m) x (9 m - 0.5 m) = 3.5 m x 8.5 m = 29.75 m².

• A. 99
• B. 90
• C. 95
• D. 100Fun & Trivia

Explanation: Each paving stone covers 2.5 m x 2 m = 5 m², while the courtyard covers 30 m x 16.5 m = 495 m². Therefore, 495 m² ÷ 5 m² = 99 stones.

• A. Rs.150
• B. Rs.100
• C. Rs.125
• D. Rs.175

Explanation: Let the sides be 3x m and 2x m. Then 3x x 2x = 3750 m², so x² = 625 m² and x = 25 m; the sides are 75 m and 50 m, giving perimeter 250 m.

• A. 12 sq m
• B. 4√14 sq m
• C. 20 sq m
• D. 15 sq m

Explanation: The side, diagonal and the unknown breadth form a right triangle. Thus breadth = √((5 m)² - (4 m)²) = 3 m, and area = 4 m x 3 m = 12 m².

• A. 12 m, 10 m
• B. 13 m, 12 m
• C. 14 m, 11 m
• D. 15 m, 10 m

Explanation: For length L m and breadth B m, L + B = 50 m ÷ 2 = 25 m and LB = 150 m².

• A. 650 m
• B. 600 m
• C. 200 m
• D. 300 m

Explanation: The perimeter equation is 2(L + B) = 600 m. Substituting B = 100 m gives 2(L + 100 m) = 600 m, so L + 100 m = 300 m and L = 200 m.

• A. 2:5
• B. 3:4
• C. 3:5
• D. 1:2

Explanation: If the original square has side s, its area is s². Its diagonal is s√2, so the square drawn on that diagonal has area (s√2)² = 2s²; hence…

• A. 64 m
• B. 32 m
• C. 30 m
• D. 16 m

Explanation: For a square, diagonal = side x √2. Therefore, side = (8√2 m) ÷ √2 = 8 m, and perimeter = 4 x 8 m = 32 m.

• A. 300 sq m
• B. 250 sq m
• C. 200 sq m
• D. 400 sq m

Explanation: For a square, diagonal² = 2 x area. Thus area = (20 m)² ÷ 2 = 400 m² ÷ 2 = 200 m².

• A. 225 sq m
• B. 220 sq m
• C. 100 sq m
• D. 30 sq m

Explanation: The area of a square is side x side. With side 15 m, area = 15 m x 15 m = 225 m².

• A. 320 tiles
• B. 640 tiles
• C. 160 tiles
• D. 6.4 tiles

Explanation: The floor area is 8 m x 4 m = 32 m². Each tile measures 0.25 m x 0.20 m, so its area is 0.05 m²; the number of tiles is 32 m² ÷ 0.05 m² =…

• A. 34
• B. 40
• C. 68
• D. 88

Explanation: If the uncovered side is 20 ft, the other dimension is 680 ft² ÷ 20 ft = 34 ft.

• A. 40
• B. 50
• C. 120
• D. None of These

Explanation: The total perimeter is Rs 5300 ÷ Rs 26.50 per metre = 200 m, so length plus breadth is 100 m.