CBSE Class 9 Mathematics Area of Parallelograms and Triangles Assignment Set A

1 Two parallelograms are on the same base and between the same parallels. What is the ratio of their areas?
(A) 2 : 1
(B) 1 : 2
(C) 1 : 1
(D) 3 : 1
Answer : C

2 ABCD is a parallelogram and '0' is the point of int ersection of its diagonals AC and BD. If t he area of ΔAOD = 8 cm², what is the area of the ΔBOC?
(A) 2 cm²
(B) 4 cm²
(C) 8 cm²
(D) 32 cm²
Answer : C

3 The area of a trapezium is 24 cm². The distance between its parallel sides is 4 cm. If one of the parallel sides is 7 cm, what is the measure of the ot her parallel side?
(A) 5 cm
(B) 8 cm
(C) 12 cm
(D) 7 cm
Answer : A

4 The area of a square is 36 cm². 1f the side of the square is doubled, what is the ratio of area of the original square to that of the new sq uare formed?
(A) 4: 1
(B) 4: 3
(C) 1 : 4
(D) 1 : 2
Answer : C

5 The area of a rhombus is 60 cm². if one of its diagonals is 15 em, find the other diagonal.
(A) 4 cm
(B) 8 cm
(C) 10 cm
(D) 16 cm
Answer : B

6 The area of a triangle is 16 cm². if it s base is 8 cm, what is its corresponding altitude?
(A) 4 cm
(B) 8 cm
(C) 18 cm
(D) 12 cm
Answer : A

7 One of the diagonals of a quadrilateral is 16 cm. The perpendiculars drawn to it from its opposite vertices are 2.6 cm and 1.4 cm. Find its area.
(A) 32 cm²
(B) 40 cm²
(C) 26 cm²
(D) 28 cm²
Answer : A

8 The ratio of the bases of two triangles is a : b. If t he ratio of their corresponding altitudes is c :d, find the ratio of their areas (in the same order).
(A) ac : bd
(B) ad : be
(C) bd : ac
(D) be :ad
Answer : A

9 The base and corresponding altitude of a parallelogram are 18 cm and 6 cm respect ively. What is its area?
(A) 36 cm²
(B) 40 cm²
(C) 44 cm²
(D) 108 cm²
Answer : D

10 In ΔABC, AB = 8 cm. If the altitudes corresponding to AB and BC are 4 cm and 5 cm respectively, find the measure of BC.
(A) 6.4 cm
(B) 4.6 cm
(C) 5.4 cm
(D) 4.5 cm
Answer : A

11 ABCD is a trapezium whose area is a₂ - b₂. lf AB = a, DC = band AB II CD ,what is the distance between the parallel sides?
(A) (a - b)
(B) (a + b)
(C) 2(a - b)
(D) 2(a + b)
Answer : C

12 The diagonals AC and BD of a parallelogram ABCD intersect at 0. P is a point on AC such that AP = 1/4 AC. Which of the following is true?

(A) ar(ΔADP) = ar(ΔAPB)
(B) ar(ΔADP) = ar(ΔDOC)
(C) ar(ΔADP) = ar(ΔBCD)
(D) ar(ΔADP) = ar(ΔADB)
Answer : A

13 In ΔXYZ, P and Q are two points on side XZ such that XP = PQ = QZ.

Which of the following is correct?
(A) ar(ΔPXY) = ar(ΔPYZ)
(B) ar(ΔPXY) = ar(ΔPYQ) = ar(ΔQYZ)
(C) ar(ΔPYQ) = ar(flXYQ)
(D) ar(ΔQYZ) = ar(ΔXYQ)
Answer : B

14 A square PQRS and a rhombus RSTU lie on the same base RS

What is the relation between their areas?
(A) ar(PQRS) = ar(RSTU)
(B) ar(PQRS) < ar(RSTU)
(C) ar(PQRS) > ar(RSTU)
(D) ar(PQRS) = 1/2 ar(RSTU)
Answer : C

15 If E, F, G and Hare respectively the mid points of the sides of a parallelogram ABCD and ar (EFGH) = 40 cm², find the ar (parallelogram ABCD) .
(A) 40 cm²
(B) 20 cm²
(C) 80 cm²
(D) 60 cm²
Answer : C

16 If a triangle and a square are on the same base and bet ween the same parallels, What is the ratio of their areas in order?
(A) 1:3
(B) 1 :2
(C) 3: 1
(D) 1 :4
Answer : B

(17-20): Observe the figures given and choose the incorrect statements.

Answer 17: C

Answer 18: B

Answer 19: C

Answer 20: B

(21 -22): Based on the figure given, identify the true stat ements.

21
(A) ar(PQRS) = 2ar(ΔPNR)
(B) ar(PQRS) = 2ar(MNRS)
(C) ar(PQRS) = ar(MNRS)
(D) ar(MNRS) = 2a r(PQRS)
Answer : C

22
(A) ar(ΔPRS) = ar(ΔQRN)
(B) ar(ΔPQR) = ar(ΔPSR)
(C) ar(ΔQRN) = '1/2 ar(PNR)
(D) ar(ΔPM S) = ar(ΔQNR)
Answer : B

23 In a ΔABC, G is the cent roid. What is the ratio of area of ΔAGC to area of ΔABC?
(A) 1 : 2
(B) 1 : 3
(C) 1 : 4
(D) 1 : 6
Answer : B

24 A square and a rhombus are on the same base and between the same parallels. Which of the following is the ratio of their areas?
(A) 1 : 1
(B) 1 : 2
(C) 1 : 3
(D) 1 : 4
Answer : A

25 Find the area of the given quadrilateral ABCD.

(A) 36 cm²
(B) 24 cm²
(C) 48 cm²
(D) 32 cm²
Answer : A

26 In the given figure, AB║DC. Identify the triangles that have equal areas.

(A) Δ ADX, Δ ACX
(B) Δ ADX, Δ XCB
(C) Δ ACX, Δ XDB
(D) All the above
Answer : A

27 In t he given figure, ABCD is a parallelogram. If area of ΔABL is 15 cm² and area of ΔDCL is 32 cm², find the area of the parallelogram ABCD.

(A) 94 cm²
(B) 86 cm²
(C) 72 cm²
(D) 65 cm²
Answer : A

28 Which of the following figures is obtained by joining mid-points of adjacent sides of a rect angle of sides 8 em and 6 em ?
(A) A rectangle of area 24 cm²
(B) A square of area 25 cm²
(C) A trapezium of area 24 cm²
(D) A rhombus of area 24 cm²
Answer : D

29 In the given figure, ABCD is a trapezium with parallel sides AB = a cm, and CD = b cm. E and F are the mid points of non parallel sides. What is the ratio of ar (EFCD) and ar (ABFE)?

(A) b :a
(B) (a+ 3b) : (3a +b)
(C) (1 + 3b) : (3a + b)
(D) (2a + b) : (3a + b)
Answer : B

30 In the given figure, ABCD is a quadrilateral. BP║AC and BP meets DC (produced) in P. If area of the quadrilateral ABCD is 145 square units, find the area of the ΔADP.

(A ) 77 cm²
(B) 38.5 cm²
(C) 40 cm
(D) 19.25 cm²

Answer 30: B

Answer 31: B

32 AD is the median of a ΔABC and the area of ΔADC = 15 cm². Find the ar (ΔABC).
(A) 15 cm²
(B) 22.5 cm²
(C) 30 cm²
(D) 37.5 cm²
Answer : C

33 lf D, E and Fare the mid-points of the sides BC, CA and AB of a ΔABC respectively, what is the quadrilateral AFDE?

(A) A square
(B) A rectangle
(C) A parallelogram
(D) A trapezium
Answer : C

34 A triang le and a rhombus are on the same base and between the same parallels.
What is the ratio of area of triangle to that of rhombus?
(A) 1 : 1
(B) 1 : 2
(C) 1 : 3
(D) 1 : 4
Answer : B

35 Pis a point in the interior of parallelogram ABCD.
If ar (║^9m ABCD) = 18 cm², what is the value of [ar (ΔAPD) + ar (ΔCPB)] ?
(A) 9 cm²
(B) 12 cm²
(C ) 18 cm²
(D) 15 cm²
Answer : A

36 In the given figure, D is the mid-point of BC and L is the mid-point of AD. If ar (ΔABL) = x ar (ΔABC) ,whatisthevalueofx ?

(A) 2
(B) 1/2
(C) 1/4
(D) 4
Answer : C

37 Area of a parallelogram ABCD is 432 cm². If BC // AD and the distance between BC and AD is 20 cm, what is the measure of the side BC of parallelogram ABCD?
(A) 43.2 cm
(B) 1 0.8 cm
(C) 18.2 cm
(D) 21.6 cm
Answer : D

Answer 38: A

Answer 39: C

Answer 40: C

Answer 41: A

Answer 42: D

Answer 43: A

Answer 44: B

Answer 45: C

Click on link below to download CBSE Class 9 Mathematics Area of Parallelograms and Triangles Assignment Set A