#Class 9 #MCQ #Chapter_9 #area_of_paralleograms_and_triangles

#Class 9 #MCQ #Chapter_9 #area_of_paralleograms_and_triangles

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MULTIPLE CHOICE QUESTIONS
LEVEL - I
1. In which of the following figures you find two polygons on the same base and between the same
parallels?
(A) (B)
(C) (D)
2. The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8cm and
6 cm, is
(A)a rectangle of area 24 cm
2
(B) a square of area of 25 cm
2
(C) a trapezium of area 24 cm
2
(D) a rhombus of area 24 cm
2
3. In the given figure, if parallelogram ABCD and rectangle ABEM are of equal area, then
(A)perimeter of ABCD = perimeter of ABEM
MD EC
A B
(B) perimeter of ABCD < perimeter of ABEM (C) perimeter of ABCD > perimeter of ABEM
(D)perimeter of ABCD =
1
2
(perimeter of ABEM)
4. The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a
parallelogram of area equal to
(A)
1
ar(ABC)
2
(B)
1
ar(ABC)
3
(C)
1
ar(ABC)
4
(D)ar(ABC)
5. Two parallelograms are on equal base and between the same parallels. The ratio of their areas is
(A)1 : 2 (B) 1 : 1 (C) 2 : 1 (D) 3 : 1
6. ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD
(A)is a rectangle
(B) is always a rhombus
(C) is a parallelogram
(D)need not be any of (A), (B) or (C)Maths Learning Centre, Jalandhar
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2. Maths Learning Centre, Jalandhar
Complete Video Lectures are available at
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7. In the given figure,  
2
ar ABC 27cm  and EF || BC. Find the area of ||
gm
(BCDE).
A
B C
DE F
(A) 54 cm
2
(B) 12 cm
2
(C) 60 cm
2
(D) 50 cm
2
8. Given parallelogram ABCF and EBCD are on the same base BC and between the same parallels
BC and AF. Given ar(EBCD) = 15 square cm, then ar(ABCF) is
(A)30 sq. cm. (B) 7.5 cm
2
(C) 15 sq. cm. (D) None of these
9. If ar(||gm ABCD) = 25 cm
2
and to the same base CD, a BCD is given such that
ar(BCD) = x cm
2
, then the value of x is :
(A)25 cm
2
(B) 50 cm
2
(C) 12.5 cm
2
(D) None of these
10. Given a quadrilateral ABCD, BE is drawn parallel to AC meeting DC produced at E. Also
ar(ADC) = 10 cm
2,
, ar(ABC) = 7 cm
2
. Then ar(ADE) will be
(A)10 cm
2
(B) 7 cm
2
(C) 17 cm
2
(D) None of these
11. In the given figure, ar(ACB) = ar(ADB), then
(A)CO = DO (B) CO > OD (C) CO < OD (D) None of these
12. In the figure, area ABC = 27 cm
2
and EF || BC. Find area of ||
gm
(ABCF).
A
B C
DE F
(A) 54 cm
2
(B) 12 cm
2
(C) 60 cm
2
(D) 50 cm
2
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3. Maths Learning Centre, Jalandhar
Complete Video Lectures are available at
https://www.youtube.com/@MathematicsOnlineLectures Class IX: Areas of Parallelograms and Triangles Mathematics
13. Given a triangle ABC and E is mid-point of median AD of ABC. If ar(BED) = 20 cm
2
. Then
ar(ABC) is
(A)10 cm
2
(B) 5 cm
2
(C) 60 cm
2
(D) 80 cm
2
14. In the given figure, ABCD and ABFE are parallelogram and ar(quad. EABC) = 17 cm
2
,
ar (parallelogram ABCD) = 25cm
2
, then ar(BCF) is
(A)4 cm
2
(B) 8 cm
2
(C) 4.8 cm
2
(D) 6 cm
2
15. In a parallelogram ABCD, AB = 8 cm. The altitudes corresponding to sides AB and AD are
respectively 4 cm and 5 cm. then AD is ____
(A) 6 cm (B) 6.5 cm (C) 6.4 cm (D) 7 cm
16. In the given figure, ABCD is rectangle with AB = 5 cm, and BC = 3 cm. then the area of the
parallelogram ABEF.
F D E C
BA 5 cm
3
c
m
(A) 10 cm
2
(B) 20 cm
2
(C) 15 cm
2
(D) 25 cm
2
17. In the given figure, ABCD is a ||gm and E is the mid-point of BC. Also, DE and AB when produced
meet at F. Then,
D
C
BA
E
F
(A)
3
2
AF AB (B) 2AF AB (C) AF = 3AB (D)
2 2
2AF AB
18. ABCD is a trapezium in which AB || DC and DC = 40 cm, AB = 60 cm. If X, Y are the midpoints
of AD and BC respectively, then area (trap.DCYX) : area(trap.XYBA) is
D
A B
C
X Y
(A) 9 : 11 (B) 2 : 5 (C) 11 : 9 (D) 5 : 2Maths Learning Centre, Jalandhar
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4. Maths Learning Centre, Jalandhar
Complete Video Lectures are available at
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19. In the given figure, ABCD is a ||gm in which AB = CD = 5 cm and BD  DC such that BD = 6.8
cm. Then, the area of ||gm ABCD is equal to
5 cmA
B
D
C5 cm
6.8cm
(A) 17 cm
2
(B) 25 cm
2
(C) 34 cm
2
(D) 68 cm
2
20. The lengths of the diagonals of a rhombus are 12 cm and 16 cm. The area of the rhombus is
(A) 192 cm
2
(B) 96 cm
2
(C) 64 cm
2
(D) 80 cm
2
21. Two parallel sides of a trapezium are 12 cm and 8 cm long and the distance between them is 6.5 cm.
The area of the trapezium is
(A) 74 cm
2
(B) 32.5 cm
2
(C) 65 cm
2
(D) 130 cm
2
22. In the given figure ABCD is a trapezium such that
A B
C
L MD
5
c
m
5
cm
4
c
m
4
c
m
7 cm
AL  DC and BM  DC. If AB = 7 cm,
BC = AD = 5 cm and AL = BM = 4 cm, then
ar(trap. ABCD) = ?
(A) 24 cm
2
(B) 40 cm
2
(C) 55 cm
2
(D) 27.5 cm
2
23. In a quadrilateral ABCD, it is given that BD = 16 cm. If AL  BD
and CM  BD such that AL = 9 cm and CM = 7 cm, then ar(quad.
ABCD) = ?
(A) 256 cm
2
L
M
D
A
B
C
(B) 128 cm
2
(C) 64 cm
2
(D) 96 cm
2
24. In the given figure, ABCD is a parallelogram in which BDC = 45
o
and BAD = 75
o
. Then
is equal toCBD
D
C
BA
75
o
45
o
(A) 45
o
(B) 55
o
(C) 60
o
(D) 75
oMaths Learning Centre, Jalandhar
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5. Maths Learning Centre, Jalandhar
Complete Video Lectures are available at
https://www.youtube.com/@MathematicsOnlineLectures Class IX: Areas of Parallelograms and Triangles Mathematics
25. In the given figure, ABCD is a parallelogram, M is the mid-point of BD and BD bisects B as well
as D. Then, ?AMB 
D
C
B
M
A
(A) 45
o
(B) 60
o
(C) 90
o
(D) 30
o
26. In the given figure, area (parallelogram ABCD) = 48 cm
2
and FC || AB. Find ar(ABE).
A B
CD EF
(A) 12 cm
2
(B) 24 cm
2
(C) 18 cm
2
(D) 8 cm
2
.
27. The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O such that
30 and 70 . Then is equal to
o o
DAC AOB DBC    
D
C
B
O
A
30
o
70
o
(A) 40
o
(B) 35
o
(C) 45
o
(D) 50
o
28. ABCD is a rhombus in which OCD = 60
o
. Then, AC : BD = ?
A
B
C
D60
o
O
(A)
1: 3 (B) 3 : 2 (C)3 :1 (D)3 : 2
29. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD.
Then the ar(APB) is
(A) ar(BPC) (B) ar( BQC) (C) ar( CPB) (D) None of theseMaths Learning Centre, Jalandhar
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6. Maths Learning Centre, Jalandhar
Complete Video Lectures are available at
https://www.youtube.com/@MathematicsOnlineLectures Class IX: Areas of Parallelograms and Triangles Mathematics
30. In Figure, E is any point on median AD of a ABC then the ar(ABE) is
D
CB
A
Fig.2
E
(A) ar(BEC) (B) ar( ACE) (C) ar( DEC) (D) ar( DAC)
31. In Figure, ABC and ABD are two triangles on the same base AB. If line segment CD is
bisected by AB at O, then the ar(ABC) is
A B
D
C
O
Fig.3
(A) ar(ABD) (B) ar( AOC) (C) ar( BOD) (D) ar( BOC)
32. D and E are points on sides AB and AC respectively of ABC such that ar(DBC) = ar(EBC)
then DE parallel to
(A) BC (B) BE (C) CF (D) CE
33. ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y then
ar(ADX) is
(A) ar(ADY) (B) ar( BDY) (C) ar( ACY) (D) ar( BCY)
34. If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio
of the area of the triangle to the area of the parallelogram is
(A) 1 : 2 (B) 1 : 3 (C) 1 : 4 (D) 3 : 4
35. In the given figure ABCD and ABFE are parallelograms such that ar(quad. EABC) = 17 cm
2
and
ar(||gm ABCD) = 25 cm
2
. Then, ar(BCF) = ?
BA
ED FC
(A) 4 cm
2
(B) 4.8 cm
2
(C) 6 cm
2
(D) 8 cm
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7. Maths Learning Centre, Jalandhar
Complete Video Lectures are available at
https://www.youtube.com/@MathematicsOnlineLectures Class IX: Areas of Parallelograms and Triangles Mathematics
36. In a ||gm ABCD, if P and Q are midpoints of AB and CD respectively
and ar(|| gm ABCD) = 16 cm
2
, then ar(||gm APQD) = ?
A P
B
C
QD
(A) 8 cm
2
(B) 12 cm
2
(C) 6 cm
2
(D) 9 cm
2
37. The area of quadrilateral ABCD in the given figure is
B
C
D
A
17 cm
9
c
m
8
c m
(A)
2
57cm (B) 108 cm
2
(C) 114 cm
2
(D) 195 cm
2
38. The area of trapezium ABCD in the given figure is
D
A
8 cm
8 cm
17 cm
15 cm
B
C
(A) 62 cm
2
(B) 93 cm
2
(C) 124 cm
2
(D) 155 cm
2
39. In the given figure, ABCD is a ||gm in which diagonals AC and BD intersect at O. If ar(||gm ABCD)
is 52 cm
2
, then the ar(OAB) = ?
A B
CD
O
(A) 26 cm
2
(B) 18.5 cm
2
(C) 39 cm
2
(D) 13 cm
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40. In the given figure ABC is right angled at B in which BC = 15 cm, and CA = 17 cm. Find the area
of acute-angled triangle DBC, it being given that AD || BC.
A
B C
D
(A) 60 cm
2
(B) 10 cm
2
(C) 65 cm
2
(D) 50 cm
2
.
LEVEL - II
1. The parallel sides of a trapezium are a and b respectively. The line joining the mid-points of its non-
parallel sides will be
(A)  
1
2
a b (B)  
1
2
a b (C)
 
2ab
a b
(D) ab
2. In a trapezium ABCD, if E and F be the mid-points of the diagonals AC and BD respectively. Then,
EF = ?
E
A B
CD
F
(A)
1
2
AB (B)
1
2
CD (C)  
1
2
AB CD (D)  
1
2
AB CD
3. In the given figure, AD is a median of ABC and E is the mid-point of AD. If BE is joined and
produced to meet AC in F, then AF = ?
A
DB C
F
E
(A)
1
2
AC (B)
1
3
AC (C)
2
3
AC (D)
3
4
ACMaths Learning Centre, Jalandhar
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9. Maths Learning Centre, Jalandhar
Complete Video Lectures are available at
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4. ABC and BDE are two equilateral triangles such that D is the midpoint of BC and DE || AC.
Then, ar(BDE) : ar (ABC) = ?
D
C
E
B
A
(A) 1 : 2 (B) 1 : 4 (C) 3 : 2 (D) 3 : 4
5. In ABC, if D is the midpoint of BC and E is the midpoint of AD, then ar(BED)=?
D
C
E
B
A
(A)  
1
2
ar ABC (B)  
1
3
ar ABC (C)  
1
4
ar ABC (D)  
2
3
ar ABC
6. The vertex A of ABC is joined to a point D on BC. If E is the midpoint of AD, then ar(BEC) =?
D
C
E
B
A
(A)  
1
2
ar ABC (B)  
1
3
ar ABC (C)  
1
4
ar ABC (D)  
1 6
ar ABCMaths Learning Centre, Jalandhar
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10. Maths Learning Centre, Jalandhar
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7. In ABC, it is given that D is the midpoint of BC; E is the midpoint of BD and O is the midpoint of
AE. Then,  ?ar BOE 
D
C
O
B
A
E
(A)  
1
3
ar ABC (B)  
1
4
ar ABC (C)  
1
6
ar ABC (D)  
1 8
ar ABC
8. In the figure, AOB = 90°, AC = BC, OA = 12 cm and OC = 6.5 cm. Find the area of AOB.
A
B
O
C
6.5 cm
12 cm
(A) 15 cm
2
(B) 13 cm
2
(C) 45 cm
2
(D) 30 cm
2
9. In the given figure ABCD is a trapezium in which AB || DC
such that AB = a cm and DC = b cm. If E and F are the
midpoints of AD and BC respectively. Then ar(ABFE) : ar
(EFCD) = ?
(A) a : b
A B
CD
E F
a
b
(B) (a + 3b) : (3a + b) (C) (3a + b) : (a + 3b)
(D) (2a + b) : (3a + b)
10. In the parallelogram ABCD, the sides AB is produced to the point X, so that BX = AB. The line
DX cuts BC at E. Area of AED = ?
(A) 2  area(CEX) (B) 1/2  area(CEX) (C) area (CEX) (D) 1/3  area(CEX).Maths Learning Centre, Jalandhar
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11. In ABC, D is the mid-point of AB. P is any point of BC. CQ || PD meets AB in Q. Then area
of (BPQ) is equal to
(A) 3/2 area of (ABC) (B) 1/2 area of (ABC)
(C) 5/2 area of (ABC) (D) 1/4 area of (ABC)
ONE OR MORE THAN ONE CORRECT
This section contains multiple choice questions. Each question has 4 choices (A), (B), (C), (D), out
of which ONE or MORE is correct. Choose the correct options.
12. In triangle ABC; D, E, F are points of trisection of BC, AC and AB respectively. Which of the
following statement is true ?
(A) Area (EDC) = 2/9 area (ABC)
A
B CD
E
F
(B) Area (FBD) = 2/7 area (AFDC)
(C) Area (DEF) = 2/9 area(ABC)
(D) Area (EDC + DBF + AFE) = 2 area(DEF).
13. Sides of ABC are subdivided into four equal parts. Areas of D
1
E
2
F
3
and ABC are in the ratio–
A
B C
F
1
F
2
F
3
E
1
E
2
E
3
D
1D
2D
3
(A) 3 : 8 (B) 3 : 16 (C) 9 : 16 (D) 9 : 24
14. D is the mid point of side AB of the triangle ABC, E is mid-point of CD and F is mid-point of AE.
Area of AED is not equal to
(A) 2  area (ABC) (B) 1/8  area (ABC)
(C) 1/2  area (ABC) (D) 1/4  area (ABC)
15. In the given figure, BD = DE = EC. Mark the correct option(s)
(A)ar(ΔABD) ar(ΔAEC)
BD EC
A
(B)ar(ΔABE) ar(ΔADC)
(C)
1
ar(ΔADE) ar(ΔABC)
2

(D)
2
ar(ΔABE) ar(ΔABC)
3
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MATRIX MATCHING TYPE QUESTIONS
Question contains statements given in two columns, which have to be matched. The statements in Column I are
labeled A, B, C and D, while the statements in Column II are labeled p, q, r, s and t. Any given statement in Column
I can have correct matching with ONE OR MORE statements(s) in Column II.
16. In figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE
intersects BC at F, match them correctly.
A
B
C
D
E
F
Column–I Column–II
(A) ar(BDE) (p)
1
4
ar(ABC)
(B) ar(BDE) (q)
1
2
ar(BAE)
(C) ar(ABC) (r) 2ar(BEC)
(D) ar(BFE) (s) ar(AFD)
17. In figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the
sides BC, CA and AB respectively. Line segment AX DE meets BC at Y. Match them correctly..
A
B C
D E
F
G
Y
N
M
X
Column–I Column–II
(A)MBC (p) congruent ABD
(B) ar(BYXD) (q) 2ar(MBC)
(C) ar(BYXD) (r) ar(ABMN)
(D) ar(CYXE) (s) 2ar(FCB)Maths Learning Centre, Jalandhar
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13. Maths Learning Centre, Jalandhar
Complete Video Lectures are available at
https://www.youtube.com/@MathematicsOnlineLectures Class IX: Areas of Parallelograms and Triangles Mathematics
INTEGER TYPE QUESTIONS
The answer to each of the questions is a single-digit integer, ranging from 0 to 9.
18. X and Y are respectively two points on the sides DC and AD of the parallelogram ABCD. The
area of ABX is equal to k times area of BYC. Find the value of k.
19. In a ABC, E is the mid-point of median AD. Then area of (BED) is equal to k/4 times area of
ABC. Find the value of k.Maths Learning Centre, Jalandhar
Maths Learning Centre, Jalandhar
Maths Learning Centre, Jalandhar
Maths Learning Centre, Jalandhar
Maths Learning Centre, Jalandhar
https://www.youtube.com/@MathematicsOnlineLectures
https://www.youtube.com/@MathematicsOnlineLectures
https://www.youtube.com/@MathematicsOnlineLectures
https://www.youtube.com/@MathematicsOnlineLectures