Mathematics Class IX

Question 1 of 50

1. Question
1 point(s)
Two parallelograms are on the same base and between the same parallels. The ratio of their areas is-
- $ 1:2$
- $ 1:1$
- $ 2:1$
- $ 3:1$
Correct

Incorrect

Hint

Ratio is $1:1$
Question 2 of 50

2. Question
1 point(s)
A triangle and a parallelogram are on the same base and between the same parallels. The ratio of the areas of triangle and parallelogram is-
- $1:2$
- $ 1:1$
- $ 2:1$
- $ 3:1$
Correct

Incorrect

Hint

Ratio is $1:2$
Question 3 of 50

3. Question
1 point(s)
If two triangles are congruent, then which of the following is true?
- They have same perimeter.
- They have same area.
- Their corresponding sides are of same length
- All of the above
Correct

Incorrect

Hint

All of the above are correct
Question 4 of 50

4. Question
1 point(s)
The median of a traingle divides it into two-
- Congruent Triangles
- Isosceles Triangles
- Triangles of equal areas
- Right triangles
Correct

Incorrect

Hint

Median divides a triangle into two triangles which are equal in area.
Question 5 of 50

5. Question
1 point(s)
A single diagonal of a parallelogram divides it into two triangles which are-
- Equilateral triangles
- Equal in area
- Isosceles triangles
- Unequal in area
Correct

Incorrect

Hint

A single diagonal of a parallelogram divides it into two triangles which are equal in area.
Question 6 of 50

6. Question
1 point(s)
Which of the following is NOT true?
- Figures with equal areas are congruent
- Figures with equal area are not congruent
- Congruent figures have equal area
- Diagonals of parallelogram forms four triangles
Correct

Incorrect

Hint

Figures with equal area may or may not be congruent.
Question 7 of 50

7. Question
1 point(s)
Diagonals of a parallelogram divides it into four-
- triangles of equal area
- congruent triangles
- Isosceles triangles
- Right triangles
Correct

Incorrect

Hint

Diagonals of a parallelogram divides it into four triangles of equal area.
Question 8 of 50

8. Question
1 point(s)
What is the formula of area of trapezium?
- $\dfrac{ height}{(difference of its parallel sides) \times 2} $
- $\dfrac{(difference of its parallel sides) \times height}{2} $
- $\dfrac{ height}{(sum of its parallel sides) \times2} $
- $\dfrac{(sum of its parallel sides) \times height}{2} $
Correct

Incorrect

Hint

Area of trapezium is $\dfrac{(sum of its parallel sides) \times height}{2}$
Question 9 of 50

9. Question
1 point(s)
Parallelograms on equal base and between the same parallels are-
- Equal in area
- Congruent
- Unequal in area
- Identical
Correct

Incorrect

Hint

Parallelograms on equal base and between the same parallels are equal in area.
Question 10 of 50

10. Question
1 point(s)
Let ABC be the triangle formed by joining the mid points of triangle DEF. If area of triangle DEF is 36 sq. units, then what is the area of triangle ABC?
- 36 sq. units
- 18 sq. units
- 20 sq. units
- 9 sq. units
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of ABC&=\dfrac{1}{2} area of DEF \\ area of ABC &= 18 \end{split}\end{equation*}$
Question 11 of 50

11. Question
1 point(s)
Which of the following is NOT true?
- The area of rhombus is half the product of the lengths of its diagonals.
- Triangles on same bases and between the same parallels are equal in area.
- The area of parallelogram is the product of its base and the corresponding altitude.
- None of the above
Correct

Incorrect

Hint

All of the above are correct
Question 12 of 50

12. Question
1 point(s)
If each diagonal of a quadrilateral separates it into two triangles of equal area, then the quadrilateral is a-
- Parallelogram
- Square
- Rectangle
- All of the above
Correct

Incorrect

Hint

This is true in all the above figures.
Question 13 of 50

13. Question
1 point(s)
If a triangle and a square are on the same base and between the same parallels then the ratio of area of square to the area of the triangle is-
- $ 1:2$
- $ 1:1$
- $ 2:1$
- $ 3:1$
Correct

Incorrect

Hint

Ratio is $2:1$
Question 14 of 50

14. Question
1 point(s)
If a planar region formed by a figure A is made up of two non-overlapping planar regions formed by figures B and C, then
- ar(A) > ar(B) + ar(C)
- ar(A) = ar(B) + ar(C)
- ar(A) < ar(B) + ar(C)
- None of the above
Correct

Incorrect

Hint

ar(A) = ar(B) + ar(C)
Question 15 of 50

15. Question
1 point(s)
In triangle DEF, Q is the centroid. What is the ratio of area of triangle DEF to area of triangle DQF?
- $ 1:3$
- $ 3:1$
- $ 1:4$
- $ 4:1$
Correct

Incorrect

Hint

Ratio is $3:1$
Question 16 of 50

16. Question
1 point(s)
In a triangle PQR, let A, B and C be the mid points of sides PQ, QR and PR respectively. If the area of triangle ABC is 24 sq. units, then what is the area of triangle PQR?
- 48 sq. units
- 24 sq. units
- 12 sq. units
- 26 sq. units
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of ABC&=\dfrac{1}{2} area of PQR \\ 48&=area of PQR \end{split}\end{equation*}$
Question 17 of 50

17. Question
1 point(s)
A, B, C and D are respectively the mid-points of the sides of a parallelogram PQRS. The ratio of area of parallelogram PQRS to the area of parallelogram ABCD is-
- $ 1:2$
- $ 1:1$
- $ 1:3$
- $ 2:1$
Correct

Incorrect

Hint

Ratio is $2:1$
Question 18 of 50

18. Question
1 point(s)
What is the area of rhombus whose diagonals are 4cm and 8cm?
- 8cm²
- 16cm²
- 32cm²
- 64cm²
Correct

Incorrect

Hint

$\dfrac{1}{2} \times 4 \times 8 = 16cm^{2}$
Question 19 of 50

19. Question
1 point(s)
Two triangles are on the same base and are between same parallels. Which of the following is true?
- Their areas are same.
- They are both congruent.
- They have same perimeter.
- None of the above
Correct

Incorrect

Hint

Two triangles on the same base and between same parallels have same area.
Question 20 of 50

20. Question
1 point(s)
A triangle and a rhombus are on the same base and between the same parallels. The ratio of the areas of triangle and rhombus is-
- $1:2$
- $ 1:1$
- $ 2:1$
- $ 3:1$
Correct

Incorrect

Hint

Ratio is $1:2$
Question 21 of 50

21. Question
1 point(s)
In a triangle ABC, AD is the altitude on side BC. If BC is 5cm and AD is 4cm, then find the area of triangle.
- 20cm²
- 15cm²
- 10cm²
- 5cm²
Correct

Incorrect

Hint

$\dfrac{1}{2} \times 4 \times 5 = 10cm^{2}$
Question 22 of 50

22. Question
1 point(s)
In a triangle DEF, DA is the altitude on side EF. If EF is 7cm and DA is 3cm, then find the area of triangle.
- 21cm²
- 5.25cm²
- 42cm²
- 10.5cm²
Correct

Incorrect

Hint

$\dfrac{1}{2} \times 7 \times 3 = 10.5cm^{2}$
Question 23 of 50

23. Question
1 point(s)
In a triangle ABC, BD is the altitude on side AC. If AC is 4.5cm and BD is 7cm, then find the area of triangle.
- 15.75cm²
- 31.5cm²
- 63cm²
- None of the above
Correct

Incorrect

Hint

$\dfrac{1}{2} \times 4.5 \times 7 = 15.75cm^{2}$
Question 24 of 50

24. Question
1 point(s)
What is the area of rhombus whose diagonals are 2m and 50cm?
- 1m²
- 0.5m²
- 2m²
- 0.5cm²
Correct

Incorrect

Hint

$\dfrac{1}{2} \times 2 \times 0.5 = 0.5m^{2}$
Question 25 of 50

25. Question
1 point(s)
P, Q, R and S are respectively the mid-points of the sides of a parallelogram ABCD. The ratio of area of parallelogram PQRS to the area of parallelogram ABCD is-
- $ 2:1$
- $ 1:1$
- $ 1:2$
- $ 3:1$
Correct

Incorrect

Hint

Ratio is $1:2$
Question 26 of 50

26. Question
1 point(s)
The trapezium ABCD has a height of 5cm. If the parallel sides are 4cm and 6cm respectively, then find the area of trapezium.
- 20cm²
- 30cm²
- 50cm²
- 25cm²
Correct

Incorrect

Hint

$\dfrac{1}{2} \times 5 \times (10) = 25cm^{2}$
Question 27 of 50

27. Question
1 point(s)
The trapezium PQRS have parallel sides of 7cm and 5cm respectively. If the height of trapezium is 9cm, then find the area of trapezium.
- 54cm²
- 108cm²
- 63cm²
- 45cm²
Correct

Incorrect

Hint

$\dfrac{1}{2} \times 9 \times (12) = 54cm^{2}$
Question 28 of 50

28. Question
1 point(s)
The diagonals of parallelogram ABCD intersect each other at O. If the area of triangle AOB is 14cm², then what is the area of parallelogram?
- 56cm²
- 14cm²
- 28cm²
- 112cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle AOB&=\dfrac{1}{4} area of parallelogram ABCD \\ 56&=area of parallelogram ABCD \end{split}\end{equation*}$
Question 29 of 50

29. Question
1 point(s)
In trapezium PQRS, PQ and SR are two parallel sides . If the area of triangle PQS and its height is 24cm² and 6cm respectively, then what is the length of side PQ?
- 3cm
- 8cm
- 4cm
- 6cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle PQS &= \dfrac{1}{2} \times 6 \times PQ \\ 8cm &=PQ \end{split}\end{equation*}$
Question 30 of 50

30. Question
1 point(s)
The figure obtained by joining the mid-points of the adjacent sides of a rectangle is-
- Square
- Rectangle
- Rhombus
- Trapezium
Correct

Incorrect

Hint

The figure obtained by joining the mid-points of the adjacent sides of a rectangle is a rhombus.
Question 31 of 50

31. Question
1 point(s)
The diagonals of parallelogram ABCD intersect each other at O. If the area of parallelogram is 32cm², then what is the area of triangle BOC?
- 32cm²
- 8cm²
- 16cm²
- 64cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle BOC&=\dfrac{1}{4} area of parallelogram ABCD \\ area of triangle BOC&=8 \end{split}\end{equation*}$
Question 32 of 50

32. Question
1 point(s)
The base and corresponding altitude of a parallelogram are 12cm and 4 cm respectively. What is the area of parallelogram?
- 12cm²
- 24cm²
- 48cm²
- 96cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of parallelogram &= 12 \times 4 \\ area of parallelogram &=48cm^{2} \end{split}\end{equation*}$
Question 33 of 50

33. Question
1 point(s)
In parallelogram PQRS, PQ and SR are parallel to each other. If the altitude to the side PQ is 15cm and area of parallelogram is 60cm², then what is the length of SR?
- 15cm
- 16cm
- 12cm
- 4cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of parallelogram PQRS&= altitude \times SR \\ 4 &=SR \end{split}\end{equation*}$
Question 34 of 50

34. Question
1 point(s)
In a parallelogram ABCD, diagonals intersect each other at O. If the area of triangle COD is 22cm², then what is the area of triangle DCB?
- 44cm²
- 22cm²
- 11cm²
- None of the above
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle COD&=\dfrac{1}{2} area of triangle DCB \\ 44&=area of triangle DCB \end{split}\end{equation*}$
Question 35 of 50

35. Question
1 point(s)
Triangle ABC and parallelogram BCDE are on the same base and between the same parallels. If the area of triangle ABC is 17cm², then what is the area of parallelogram BCDE?
- 17cm²
- 34cm²
- 19cm²
- 68cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle ABC&=\dfrac{1}{2} area of parallelogram BCDE \\ 34&=area of parallelogram BCDE \end{split}\end{equation*}$
Question 36 of 50

36. Question
1 point(s)
If the area of parallelogram PQRS is 42cm², then what is the area of triangle PRQ?
- 42cm²
- 84cm²
- 21cm²
- 10.5cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle PRQ&=\dfrac{1}{2} area of parallelogram PQRS \\ area of triangle PRQ&=21 \end{split}\end{equation*}$
Question 37 of 50

37. Question
1 point(s)
If AD is median of the triangle ABC, then what is the ratio of area of triangle ABD and ACD?
- $ 1:2$
- $ 1:1$
- $ 2:1$
- $ 3:1$
Correct

Incorrect

Hint

Ratio is $1:1$
Question 38 of 50

38. Question
1 point(s)
Let ABC be the triangle formed by joining the mid points of triangle DEF. If area of triangle DEF is 54 sq. units, then what is the area of triangle ABC?
- 27 sq. units
- 54 sq. units
- 12 sq. units
- 26 sq. units
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of ABC&=\dfrac{1}{2} area of DEF \\ area of ABC &= 27 \end{split}\end{equation*}$
Question 39 of 50

39. Question
1 point(s)
In trapezium ABCD, AB and DC are two parallel sides . If the area of triangle ABD is 58cm² and AB=8cm, then what is the height of triangle ABC?
- 29cm
- 14.5cm
- 20cm
- 14.5cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle ABD&=\dfrac{1}{2} \times AB \times height\\14.5 &=height \end{split}\end{equation*}$
Question 40 of 50

40. Question
1 point(s)
What is the area of parallelogram ABCD if the area of triangle ACB is 52cm²?
- 26cm²
- 13cm²
- 104cm²
- 65cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle ACB&=\dfrac{1}{2} area of parallelogram ABCD \\104 &=area of parallelogram ABCD \end{split}\end{equation*}$
Question 41 of 50

41. Question
1 point(s)
Two triangles ABC and DEF are congruent in nature. Which of the following is true?
- AB=DE
- BC=EF
- The area of triangle ABC is equal to the area of triangle DEF.
- All of the above
Correct

Incorrect

Hint

All of the above are correct
Question 42 of 50

42. Question
1 point(s)
Two triangles ABC and DEF have same area. Which of the following is true?
- Corresponding sides of triangles are equal
- Triangles may or may not be congruent.
- Corresponding angles are equal
- All of the above
Correct

Incorrect

Hint

Two triangles of same area may or may not be congruent.
Question 43 of 50

43. Question
1 point(s)
The trapezium ABCD has a height of 7cm. If the parallel sides are 2cm and 3cm respectively, then find the area of trapezium.
- 35cm²
- 17.5cm²
- 14cm²
- 21cm²
Correct

Incorrect

Hint

$\dfrac{1}{2} \times 7 \times (5) = 17.5cm^{2}$
Question 44 of 50

44. Question
1 point(s)
The medians of triangle DEF intersect each other at O. If the area of triangle DOF is 5cm², then what is the area of triangle DEF?
- 5cm²
- 10cm²
- 15cm²
- 30cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle DOF&=\dfrac{1}{3} area of triangle DEF \\ 15&=area of triangle DEF \end{split}\end{equation*}$
Question 45 of 50

45. Question
1 point(s)
The medians of triangle ABC intersect each other at O. If the area of triangle ABC is 27cm², then what is the sum of area of triangle AOC and BOC?
- 27cm²
- 9cm²
- 54cm²
- 18cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle AOC + area of triangle BOC&=\dfrac{2}{3} area of triangle ABC \\ area of triangle AOC + area of triangle BOC&=18 \end{split}\end{equation*}$
Question 46 of 50

46. Question
1 point(s)
Triangle ABC and parallelogram BCDE are on the same base and between the same parallels. If the area of parallelogram BCDE is 32cm², then what is the area of triangle ABC?
- 32cm²
- 8cm²
- 45cm²
- 16cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle ABC&=\dfrac{1}{2} area of parallelogram BCDE \\ area of triangle ABC&=16 \end{split}\end{equation*}$
Question 47 of 50

47. Question
1 point(s)
In a parallelogram PQRS, diagonals intersect each other at O. If the area of triangle SQR is 42cm², then what is the area of triangle POQ?
- 42cm²
- 21cm²
- 10.5cm²
- None of the above
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle POQ&=\dfrac{1}{2} area of triangle SQR \\ area of triangle POQ&=21 \end{split}\end{equation*}$
Question 48 of 50

48. Question
1 point(s)
What is the area of triangle PQR if the area of triangle QCR is 32cm² and RC is the median?
- 32cm²
- 18cm²
- 64cm²
- 16cm²
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} area of triangle QCR&=\dfrac{1}{2} area of triangle PQR \\ 64&=area of triangle PQR \end{split}\end{equation*}$
Question 49 of 50

49. Question
1 point(s)
In a triangle ABC, AD and BE are two medians. If the area of triangle ACD is 17cm², then what is the area of triangle BEC?
- 17cm²
- 34cm²
- 8.5cm²
- Cannot be determined
Correct

Incorrect

Hint

Area of triangle ACD = Area of triangle BEC
Question 50 of 50

50. Question
1 point(s)
The trapezium PQRS have parallel sides of 8cm and 3cm respectively. If the height of trapezium is 5cm, then find the area of trapezium.
- 27.5cm²
- 40cm²
- 55cm²
- 15cm²
Correct

Incorrect

Hint

$\dfrac{1}{2} \times 5 \times (11) = 27.5cm^{2}$

Mathematics Class IX

Concept Checkers-Areas of Parallelograms and Triangles-ClassIX

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