Geometry and Mensuration

1. What is the area of a trapezoid with parallel sides 6 and 10, and height 4?

💡 Area = ½ × (sum of parallel sides) × height = ½ × (6+10) × 4 = ½ × 16 × 4 = 32.

2. What is the area of a circle with radius 7? (Use π = 22/7)

💡 Area = πr² = (22/7) × 7 × 7 = 22 × 7 = 154 square units.

3. What is the volume of a cube with side 5 cm?

💡 Volume of cube = side³ = 5³ = 5 × 5 × 5 = 125 cm³.

4. What is the volume of a rectangular box with length 4, width 3, height 5?

💡 Volume = length × width × height = 4 × 3 × 5 = 60 cubic units.

5. What is the name of a triangle with all three sides equal?

💡 An equilateral triangle has all three sides equal in length and all angles equal to 60°.

6. What is the sum of interior angles of a hexagon?

💡 Sum of interior angles = (n-2) × 180° = (6-2) × 180° = 4 × 180° = 720°.

7. What is the diagonal of a rectangle with length 3 and width 4?

💡 Using Pythagoras: diagonal = √(3² + 4²) = √(9+16) = √25 = 5.

8. In a right triangle, if one angle is 90° and another is 35°, what is the third?

💡 Third angle = 180° - 90° - 35° = 55°.

9. An angle greater than 90° but less than 180° is called?

💡 An obtuse angle measures between 90° and 180°. Acute is less than 90°, reflex is greater than 180°.

10. What is the area of a triangle with base 10 and height 8?

💡 Area of triangle = ½ × base × height = ½ × 10 × 8 = 40 square units.

11. Two angles of a triangle are 65° and 75°. What is the third angle?

💡 Third angle = 180° - 65° - 75° = 40°.

12. What is the perimeter of a circle with diameter 14? (Use π = 22/7)

💡 Circumference = πd = (22/7) × 14 = 44 units.

13. What is the Pythagorean theorem?

💡 The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse.

14. A cylinder has radius 3 and height 7. What is its volume? (Use π = 22/7)

💡 Volume = πr²h = (22/7) × 3² × 7 = 22 × 9 = 198 cubic units.

15. What is the surface area of a cube with side 4 cm?

💡 Surface area = 6 × side² = 6 × 4² = 6 × 16 = 96 cm².

Quiz Complete!