CBSE Class 9 Maths Areas of Parallelogram and Triangle MCQs

Question. In the given figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AD = 12 cm, AE = 8 cm and CF = 10 cm, then find CD.

(A) 17 cm
(B) 12 cm
(C) 10 cm
(D) 15 cm
Answer : D

Question. Parallelograms on the same base and between the same parallels are equal in
(A) Perimeter
(B) Shape
(C) Area
(D) None of these
Answer : C

Question. Find the area of a trapezium ABCD in which AB || DC, AB = 77 cm, BC = 25 cm, CD = 60 cm and DA = 26 cm.
(A) 204 cm²
(B) 1644 cm²
(C) 1645 cm²
(D) 1600 cm²
Answer : B

Question. The median of a triangle divides it into two
(A) Triangles of equal area
(B) Congruent triangles
(C) Right angled triangles
(D) Isosceles triangles
Answer : A

Question. In the given figure, ABCD is a parallelogram and P is mid-point of AB. If ar(APCD) = 36 cm², then ar(ΔABC) =

(A) 36 cm²
(B) 48 cm²
(C) 24 cm²
(D) None of these
Answer : C

Question. In the given figure, if ABCD is a parallelogram and E is the mid-point of BC, then ar(ΔDEC) = k ar(ABCD). Find k.

(A) 2
(B) 1/4
(C) 1/2
(D) 2/3
Answer : B

Question. ABC is a triangle in which D is the mid-point of BC and E is the mid-point of AD such that the area of ΔBED = K area of ΔABC. Find K

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

Question. The mid-points of the sides of a ΔABC along with any of the vertices as the fourth point make a parallelogram of area equal to
(A) (1/2)area (ΔABC)
(B) (1/3)area (ΔABC)
(C) (1/4)area (ΔABC)
(D) area (ΔABC)
Answer : A

Question. In the given figure, ABCD is a parallelogram, AL ⊥ BC, AM ⊥ CD, AL = 4 cm and AM = 5 cm. If BC = 6.5 cm, then find CD.

(A) 5.2 cm
(B) 8.7 cm
(C) 6.5 cm
(D) 3.3 cm
Answer : A

Question. In the given figure, if ar (ΔABC) = 28 cm², then ar (AEDF) =

(A) 21 cm²
(B) 18 cm²
(C) 16 cm²
(D) 14 cm²
Answer : D

Question. In the given figure, ABCD is a quadrilateral with BD = 20 cm. If AL ⊥ BD and CM ⊥ BD such that AL = 10 cm and CM = 5 cm, find the area of quadrilateral ABCD.

(A) 150 cm²
(B) 180 cm²
(C) 100 cm²
(D) 140 cm²
Answer : A

Question. The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is
(A) A rhombus of area 24 cm²
(B) A square of area 25 cm²
(C) A trapezium of area 24 cm²
(D) A rectangle of area 24 cm²
Answer : A

Question. ABCD is a rectangle with O as any point in its interior. If ar (ΔAOD) = 3 cm² and ar (ΔBOC) = 6 cm², then area of rectangle ABCD is
(A) 9 cm²
(B) 12 cm²
(C) 15 cm²
(D) 18 cm²
Answer : D

Question. The diagonals AC and BD of a parallelogram ABCD intersect each other at O. PQ is a line through O which meets BC at P and AD at Q. If ar(quad. ABPQ) = k ar (Parallelogram ABCD), then k =
(A) 1/2
(B) 4
(C) 3
(D) 1/4
Answer : A

Question. The area of a trapezium whose parallel sides are 9 cm & 16 cm and the distance between these sides is 8 cm, is
(A) 60 cm²
(B) 72 cm²
(C) 56 cm²
(D) 100 cm²
Answer : D

Question. If E, F, G and H are the mid-points of sides of a parallelogram ABCD then ar(EFGH) = ––––.

(A) (1/3)ar(ABCD)
(B) ar(ABCD)
(C) (1/2)ar(ABCD)
(D) (1/4)ar(ABCD)
Answer : C

Question. Read the statements carefully and write 'T' for true and 'F' for false.
(a) Two parallelograms on the same base and between the same parallel lines are of unequal areas.
(b) The ratio of area of rectangle and a triangle having the same base and between the same parallel is 2 : 1.
(c) The area of a parallelogram is the product of its base and the corresponding altitude
     (a      (b)    (c)
(A) F       T       F
(B) T       T       T
(C) T       F       T
(D) F       T       T
Answer : D

Question. E is any point on median AD of ΔABC. If ar (ΔABE) = 10 cm² then ar (ΔACE) is
(A) 20 cm²
(B) 5 cm²
(C) 30 cm²
(D) 10 cm²
Answer : D

Question. Two parallelograms are on same base and between same parallels. Then, the ratio of their areas is

(A) 1 : 2
(B) 1 : 1
(C) 2 : 1
(D) 3 : 1
Answer : B

Question. ABCD is a parallelogram. X and Y are the mid-points of BC and CD respectively.
Then, ar (ΔAXY) =
(A) ar (ΔDBC)
(B) (3/8)ar (||^gm ABCD)
(C) (1/2)ar (||^gm ABCD)
(D) ar (ΔCYX)
Answer : B

Question. ABCD is a parallelogram. Two lines l and m are parallel to AD. Line l meets AB and CD at P and S respectively. Line m meets AB and CD at Q and R respectively. X is any point on CD between R and S. If ar (ΔDPX) + ar(ΔCQX) = k ar(ABCD), find k.

(A) 2/3
(B) 3/2
(C) 1/2
(D) 1/3
Answer : C

Question. ABCD is a parallelogram. P is any point on CD. If ar(ΔDPA) = 15 cm² and ar (ΔAPC) = 20 cm², then ar(ΔAPB) =
(A) 15 cm²
(B) 20 cm²
(C) 35 cm²
(D) 30 cm²
Answer : C

Question. If AD is median of DABC and P is a point on AC such that ar(ΔADP) : ar(DABD) = 2 : 3, then ar(DPDC) : ar(ΔABC) is
(A) 1 : 5
(B) 5 : 1
(C) 1 : 6
(D) 3 : 5
Answer : C

Question. ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects CD at F. If area of ΔDFA is 3 cm², then find the area of parallelogram ABCD.

(A) 6 cm²
(B) 12 cm²
(C) 9 v
(D) 18 cm²
Answer : B

Question. ABCD is a parallelogram, G is the point on AB such that AG = 2GB, E is point on DC such that CE = 2DE and F is the point on BC such that BF = 2FC. Then, match the following:
    Column-I               Column-II
P. ar (ADEG)         (i) 1/6 ar (ABCD)
Q. ar (ΔEGB)        (ii) ar (ΔEDG)
R. ar (ΔEFC)        (iii) ar (GBCE)
S. ar (ΔEGB)        (iv) 1/2 ar (DEBF)
       P         Q         R        S
(A) (i)        (ii)       (iii)       (iv)
(B) (iii)       (i)       (iv)       (ii)
(C) (iii)      (ii)       (iv)        (i)
(D) (ii)       (i)        (iii)       (iv)
Answer : B

Question. Parallelograms on the same base and between the same parallels are _______ in area
(a) half
(b) one third
(c) one fourth
(d) equal

Question. If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is ______ of the area of the parallelogram.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. In the below Fig., ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

(a) 10.8
(b) 11.8
(c) 12.8
(d) 13.8

Question. In the above Fig., ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AD = 9 cm, CF = 4 cm and DC = 12 cm, find AE.
(a) 3 cm
(b) 6 cm
(c) 9 cm
(d) 2 cm

Question. In the above Fig., ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AD = 5 cm, CF = 8 cm and AE = 4 cm, find AB.
(a) 10 cm
(b) 20 cm
(c) 9 cm
(d) 12 cm

Question. If E,F,G and H are respectively the mid-points of the sides of a parallelogram ABCD, then ar(EFGH) =
(a) ar(ABCD)
(b) 1/2ar(ABCD)
(c) 1/3ar(ABCD)
(d) 1/4ar(ABCD)

Question. In the below Fig., ABCD is a parallelogram and EFCD is a rectangle, then ar (EFGH) =
(a) ar(ABCD)
(b) 1/2ar(ABCD)
(c) 1/3ar(ABCD)
(d) 1/4ar(ABCD)

Question. Two triangles on the same base (or equal bases) and between the same parallels are _______ in area.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. A median of a triangle divides it into two triangles of ______ areas.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. Area of a triangle is _______ the product of its base and the corresponding altitude.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. Area of a parallelogram is ______ the product of its base and the corresponding altitude.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. The area of a rhombus, the lengths of whose diagonals are 16 cm and 24 cm respectively, is
(a) 192 cm²
(b) 120 cm²
(c) 384 cm²
(d) none of these

Question. The area of a trapezium whose parallel sides are 9 cm and 6 cm and the distance between these sides is 8 cm is
(a) 92 cm²
(b) 120 cm²
(c) 60 cm²
(d) none of these

Question. The area of a below quadrilateral is
(a) 112 cm²
(b) 120 cm²
(c) 114 cm²
(d) none of these

Question. The area of a below quadrilateral is
(a) 150 cm²
(b) 180 cm²
(c) 100 cm²
(d) none of these

Question. D, E and F are respectively the mid-points of the sides BC, CA and AB of a ΔABC, then ar (DEF)
(a) ar(ABC)
(b) 1/2ar(ABC)
(c) 1/3 ar(ABC)
(d) 1/4 ar(ABC)

Question. D, E and F are respectively the mid-points of the sides BC, CA and AB of a ΔABC, then ar (BDEF)
(a) ar(ABC)
(b) 1/2ar(ABC)
(c) 1/3ar(ABC)
(d) 1/4ar(ABC)

Question. In a triangle ABC, E is the mid-point of median AD, then ar (BED) =
(a) ar(ABC)
(b) 1/2ar(ABC)
(c) 1/3ar(ABC)
(d) 1/4ar(ABC)

Question. In ΔABC, E is any point on median AD then ar (ABE) =
(a) ar(ACE)
(b) 1/2ar(ACE)
(c) 1/3ar(ACE)
(d) 1/4ar(ACE)

Question. ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O then ar(ABC) =
(a) ar(ABD)
(b) 1/2ar(ABD)
(c) 1/3ar(ABD)
(d) 1/4ar(ABD)

Question. In Fig. ABCD is a quadrilateral and BE || AC and also BE meets DC produced at E then the area of ΔADE is ______ to the area of the quadrilateral ABCD.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. In the above sided Fig, P is a point in the interior of a parallelogram ABCD then ar (APB) + ar(PCD) =
(a) ar(ABCD)
(b) 1/2ar(ABCD)
(c) 1/3ar(ABCD)
(d) 1/4ar(ABCD)

Question. In Fig, PQRS and ABRS are parallelograms and X is any point on side BR then ar (AX S) =
(a) ar(PQRS)
(b) 1/2ar(PQRS)
(c) 1/3ar(PQRS)
(d) 1/4ar(PQRS)

Question. In Fig, PQRS and ABRS are parallelograms and X is any point on side BR then ar (ABRS) =
(a) ar(PQRS)
(b) 1/2ar(PQRS)
(c) 1/3ar(PQRS)
(d) 1/4ar(PQRS)

Question. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD then ar (APB) =
(a) ar(BQC)
b) 1/2ar(BQC)
(c) 1/3ar(BQC)
(d) 1/4ar(BQC)

Question. In the below figure, ABCD is trapezium in which AB || DC and its diagonals AC and BD intersect at O then ar(AOD) =
(a) ar(BOC)
(b) 1/2ar(BOC)
(c) 1/3ar(BOC)
(d) 1/4ar(BOC)

Question. In the adjoining figure, ABCD is a quadrilateral in which diagonal BC = 14 cm. If AL  BD and CM  BD such that AL = 8cm and CM = 6 cm, then the area of quadrilateral is
(a) 90 cm²
(b) 95 cm²
(c) 98 cm²
(d) none of these

Question. Given figure A and figure B such that area(A) = 20 sq. units and area(B) = 20 sq. units. The
(a) figure A and B are congruent
(b) figure A and B are all not congruent.
(c) figure A and B may or may not be congruent
(d) none of these.

Question. Out of the given figures, mark which are not on the same base but between same parallels 

Question. In the given figure, BD = DE = EC. Mark the correct option 

(a) ar(ΔABD) = ar(ΔAEC)
(b) ar(ΔDBA) = ar(ΔADC)
(c) ar(ΔADE) = 1/3 ar(ΔABC)
(d) ar(ΔABE) = 2/3 ar(ΔABC)

Question. ABCDE is a pentagon. A line through B line parallel to AC meet DC produced at F.
(a) ar(ΔACB) = ar(ΔAEC)
(b) ar(ΔABF) = ar(ΔCABF)
(c) ar(ΔACF) = ar(ΔCBF)
(d) ar(ΔABF) = ar(ΔABC)

Question. In the below figure, ABCD is a parallelogram, then ar(ΔAFB) is 

(a) 16 cm²
(b) 8 cm²
(c) 4 cm²
(d) 2 cm²

Question. In the given figure, ABCD and ABFE are parallelograms and ar(quad. EABC) = 17 cm2, ar(||^gm ABCD) = 25 cm2 then ar(ΔBCF) is 

(a) 4 cm²
(b) 8 cm²
(c) 4.8 cm²
(d) 6 cm²

Question. Given ar(ΔABC) = 32cm², AD is median of ΔABC, and BE is median of ΔABD. IF BO is median of ΔABE, the ar(ΔBOE) is
(a) 16 cm²
(b) 4 cm²
(c) 2 cm²
(d) 1 cm2

Question. In the given figure, find x, if ABCD is a rhombus and AC = 4cm, ar(ABCD) = 20cm2. 

(a) 4 cm
(b) 5 cm
(c) 10 cm
(d) 2.5 cm

Question. In the given figure, find the area of rhombus ABCD if AO = 4 cm and OD = 5 cm. 

(a) 40 cm²
(b) 80 cm²
(c) 20 cm²
(d) 10 cm²

Question. The area of rhombus is 120 cm2 and one of its diagonals is 12 cm then the other diagonal is
(a) 5 cm
(b) 10 cm
(c) 20 cm
(d) 12 cm

Question. Given in triangle ABC, BE is the median of ΔABC and ar(ΔABE) = 20 cm2, then ar(ΔABC) =
(a) 40 cm²
(b) 80 cm²
(c) 20 cm²
(d) 10 cm²

Question. In the adjoining figure, ABCD is a trapezium in which AB || DC; AB = 7 cm; AD = BC = 5 cm and the distance between the parallel lines is 4 cm, then length DC =

(a) 15 cm
(b) 13 cm
(c) 11 cm
(d) 12 cm

Question. In the above figure, ABCD is a trapezium in which AB || DC; AB = 7 cm; AD = BC = 5 cm and the distance between the parallel lines is 4 cm, then the area of trap. ABCD =
(a) 40 cm²
(b) 80 cm²
(c) 20 cm²
(d) 10 cm²

Question. In the below figure, ABCD is a parallelogram; DC = 5 cm; BD = 7 cm, then the area of parallelogram ABCD is 

(a) 45 cm²
(b) 35 cm²
(c) 25 cm²
(d) 10 cm²

Question. In the above figure, ABCD is a parallelogram; AB = 10 cm; BM = 8 cm and DL = 6 cm, then AD =
(a) 15 cm
(b) 13 cm
(c) 11 cm
(d) none of these