Class 9 Mathematics (NCERT)

1. Two congruent figures always have:

• A. Different areas
• B. Equal areas
• C. Double area
• D. None of these

2. If two figures have equal areas, then they are:

• A. Always congruent
• B. Need not be congruent
• C. Always similar
• D. Equal in perimeter

3. Parallelograms on the same base and between the same parallels are:

• A. Equal in area
• B. Unequal in area
• C. Always congruent
• D. Similar

4. The area of a parallelogram is given by the formula:

• A. Base × Height
• B. 1/2 × Base × Height
• C. 2 × Base × Height
• D. Base + Height

5. If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is ________ the area of the parallelogram.

• A. Equal to
• B. Half of
• C. Double of
• D. One-third of

6. Triangles on the same base and between the same parallels are:

• A. Equal in area
• B. Congruent
• C. Unequal in area
• D. Similar

7. The median of a triangle divides it into two triangles of:

• A. Equal perimeter
• B. Equal area
• C. Congruent shapes
• D. Unequal area

8. Area of a triangle is calculated using which formula?

• A. Base × Height
• B. 1/2 × Base × Height
• C. 2 × (Base + Height)
• D. Base / Height

9. ABCD is a parallelogram. If area(ABCD) = 40 cm², then area(ΔABC) is equal to:

• A. 40 cm²
• B. 20 cm²
• C. 80 cm²
• D. 10 cm²

10. In ΔABC, AD is a median. If area(ΔABC) = 30 cm², then area(ΔABD) is:

• A. 30 cm²
• B. 15 cm²
• C. 60 cm²
• D. 10 cm²

11. If a rectangle and a parallelogram stand on the same base and between the same parallels, their areas are in the ratio:

• A. 1 : 2
• B. 2 : 1
• C. 1 : 1
• D. 1 : 4

12. If the base of a parallelogram is 8 cm and its corresponding altitude is 5 cm, its area is:

• A. 20 cm²
• B. 40 cm²
• C. 13 cm²
• D. 80 cm²

13. In ΔABC, D, E, F are mid-points of sides BC, CA, and AB respectively. The ratio of area(ΔDEF) to area(ΔABC) is:

• A. 1 : 2
• B. 1 : 3
• C. 1 : 4
• D. 1 : 8

14. Parallelogram ABCD and ΔABE lie on the same base AB and between same parallels AB and CD. If area(ΔABE) = 24 cm², find area(ABCD):

• A. 12 cm²
• B. 24 cm²
• C. 48 cm²
• D. 36 cm²

15. If the area of a parallelogram is 60 cm² and its base is 10 cm, then its altitude is:

• A. 6 cm
• B. 12 cm
• C. 30 cm
• D. 5 cm

16. The area of a rhombus with diagonals d₁ and d₂ is given by:

• A. d₁ × d₂
• B. 1/2 × d₁ × d₂
• C. 2 × d₁ × d₂
• D. 1/4 × d₁ × d₂

17. Two triangles having equal areas and a common base on the same side lie between:

• A. Perpendicular lines
• B. Intersecting lines
• C. Same parallel lines
• D. Concentric circles

18. The area of a trapezium is given by:

• A. 1/2 × (sum of parallel sides) × height
• B. (sum of parallel sides) × height
• C. 1/2 × (product of parallel sides) × height
• D. 2 × (sum of parallel sides) × height

19. In ΔABC, E is the mid-point of median AD. Then area(ΔBED) is equal to:

• A. 1/2 area(ΔABC)
• B. 1/3 area(ΔABC)
• C. 1/4 area(ΔABC)
• D. 1/8 area(ΔABC)

20. The diagonals AC and BD of a parallelogram ABCD intersect at O. Then area(ΔAOB) =

• A. area(ΔBOC)
• B. 1/4 area(ABCD)
• C. Both A and B
• D. None of these

21. If base of a triangle is doubled and altitude is halved, its area will:

• A. Double
• B. Become half
• C. Remain unchanged
• D. Quadruple

22. Parallelogram ABCD and rectangle ABEF are on the same base AB. Then:

• A. area(ABCD) > area(ABEF)
• B. area(ABCD) < area(ABEF)
• C. area(ABCD) = area(ABEF)
• D. No relation

23. In a triangle ABC, if altitude h = 6 cm and area = 24 cm², find base b.

• A. 4 cm
• B. 8 cm
• C. 12 cm
• D. 16 cm

24. ABCD is a trapezium with AB || CD. Diagonal AC and BD intersect at O. Then:

• A. area(ΔAOD) = area(ΔBOC)
• B. area(ΔAOB) = area(ΔCOD)
• C. area(ΔAOD) = area(ΔAOB)
• D. None of these

25. If ABCD is a square of side 6 cm, what is the area of ΔABC?

• A. 36 cm²
• B. 18 cm²
• C. 12 cm²
• D. 9 cm²

26. Altitude of a triangle divides it into two right triangles of:

• A. Always equal areas
• B. Equal areas only if triangle is isosceles/equilateral
• C. Always congruent
• D. Never equal areas

27. If parallel sides of a trapezium are 10 cm and 14 cm and height is 5 cm, its area is:

• A. 60 cm²
• B. 120 cm²
• C. 35 cm²
• D. 70 cm²

28. Two parallelograms have equal bases and lie between same parallel lines. The ratio of their areas is:

• A. 1 : 2
• B. 1 : 1
• C. 2 : 1
• D. 1 : 3

29. In ΔABC, D is mid-point of BC and E is mid-point of AD. Then area(ΔAEC) =

• A. 1/2 area(ΔABC)
• B. 1/4 area(ΔABC)
• C. 1/3 area(ΔABC)
• D. 1/8 area(ΔABC)

30. Can two figures be congruent if their areas are unequal?

• A. Yes
• B. No
• C. Sometimes
• D. Depends on shape