Parallelograms on the Same Base and between the Same Parallels Are Equal in Area
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Prove that two triangles on the same base (or equal bases) and between the same parallels are equal in area.
[4 MARKS]
Two figures are said to be congruent if they have:
same length of sides
same shape and size
same measure of angles
same area
PQ is a line parallel to side BC and passing through vertex A of a triangle ABC. BE || AC and CF || AB meet PQ at E and F respectively. If the base and altitude of ΔABC are 6 cm and 8 cm respectively, the area of ΔACF is ___.
12 cm2
24 cm2
48 cm2
96 cm2
- 8 cm2
- 118 cm2
- 5 cm2
- 67 cm2
If a triangle and a parallelogram are on the same base and between the same parallels, then
area of triangle = (1/4) area of parallelogram
area of triangle = (1/3)area of parallelogram
area of triangle = (1/2)area of parallelogram
area of triangle = area of parallelogram
If P is the interior point of parallelogram ABCD , the sum of area of ΔPAB and ΔPDC is as equal to ______ of the area of parallelogram ABCD
- thrice
- one-third
- half
- twice
- 50 cm2
- 20 cm2
- 100 cm2
- 30 cm2
In the given figure, ABCD and DPQR are parallelograms. Area of ABCD is equal to the area of _______.
- DPQR
- DCP
- ADR
- DRBC
In the parallelogram PQRS shown, if A is a point on the side RS, then area of parallelogram is _____times the sum of areas of ΔQRA and ΔSAP.
- 4
- 1.5
- 2
- 3
Ranjith has a field in the shape of parallelogram ABCD as shown in the figure. He knows area of triangular portions ABP and CDP are 200 m2 and 300 m2, where P is any point on edge AD. The area of the total field ABCD is 1500 m2.
True
False
In the given figure, ABCD is a parallelogram. P and Q are any two points in AB and BC respectively. Area of Δ ADQ= ___
- area ΔPBC
- area ΔDPC
- area ||gm ABCD.
- area ΔADP
Assertion : In ΔABC, median AD is produced to X such that AD = DX. Then, ABXC is a parallelogram.
Reason : Diagonals AX and BC bisect each other at right angles.
Which of the following is correct?
- If both assertion and reason are true and reason is the correct explanation of assertion
- If both assertion and reason are true but reason is not the correct explanation of assertion
- If assertion is false but reason is true
- If assertion is true but reason is false
In the given figure, ABCD is a parallelogram and PD is parallel to QC.
S1 : △APD ≅ △BQC
S2 : ar(△APD) + ar(PBCD) = ar(△BQC) + ar(CDPB)
S1 and S2 are both true and S2 is the explanation for S1
S1 and S2 are are both true and S1 is the explanation for S2
S1 is true but S2 is false
S1 is false but S2 is true
Rectangle ABCD and ||gram PQRS lie between same base and same parallels.The ratio of their areas is
1 : 2
1 : 1
1 : 3
2 : 1
In the figure shown, the area of the parallelogram shown is 60 cm2. If E, F, G, H are mid-points of sides of parallelogram , then area of the EFGH is______
- 30 cm2
- 60 cm2
- 120 cm2
- 15 cm2
In Δ ABC, D and E are the midpoints of side AB and AC. State which of the following are correct option(s).
- Area of Δ BEC and Δ BDC are equal.
- Area of Δ BDE and Δ BDC are equal.
- Area of Δ BEC and Δ CED are equal.
- Area of Δ DOB and Δ EOC are equal.
If P is the interoir point of parallelogram ABCD, prove that the sum of area of ΔPAB and ΔPDC is as equal to half of the area of parallelogram ABCD [2 MARKS]
- 2:1
- 3:1
- 2:3
- 1:2
Area of △ is ___the area of the parallelogram, if both are on equal bases and between the same parallels.
one - fourth
half
three - fourth
equal to
ABCD is a parallelogram and E and F are mid-points of AD and BC respectively. P is any point on AB. If area of ΔEDF=16 cm2, then find the area of ( ΔAEP+ ΔBFP) [3 MARKS]
In the given figure ABCD is a parallelogram. If area of parallelogram ABCD = 1728 square units, then area △ BEC = ____ square units.
- 864 square units
- 432 square units
- 1728 square units
- 400 square units
- twice
- one-third
- thrice
- half
In the given figure, ABCD is a parallelogram and PD is parallel to QC.
S1 : △APD ≅ △BQC
S2 : ar (△APD) + ar (PBCD) = ar (△BQC) + ar (CDPB)
Choose the correct option and justify your choice.
(a) S1 is true but S2 is false
(b) S1 is false but S2 is true
(c) S1 and S2 are both true and S2 is the explanation for S1
(d) S1 and S2 are both true and S1 is the explanation for S2
[ 3 marks ]
- 0.5 x sum of non-parallel sides x height
- Product of base and height
- 0.5 x sum of parallel sides x height
- twice the product of base and height
ABCD is a parallelogram in which CD is produced to P. DC = 6 cm and height BQ = 4 cm. Find the area of △ APB
- 6 cm2
- 12 cm2
- 24 cm2
- 48 cm2
In the given figure, PQRS is a rectangle of area 35cm2. Find the area of ΔEFT.
- 35cm2
- 70cm2
- 17.5cm2
- 60cm2
In the figure if area of parallelogram ABCD is 30 cm2, then area of ΔAEB is equal to ______.
- 10 cm2
- 25 cm2
- 15 cm2
- 35 cm2
Δ ABP and parallelogram PABC are between the same parallel lines. If the area of parallelogram PABC is 24 cm2, then the area of Δ ABP is
- 48 cm2
- 6 cm2
- 32 cm2
- 12 cm2
. If the area of || gram is 120 sq.cm , what is the ar(△) which is between the same base and same parallels?
120 sq cm
60 sq cm
240 sq cm
320 sq cm