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question_answer1)
In the given figure, ABCD is a parallelogram, \[AE\bot DC\]and \[CF\bot AD.\]If AD = 12 cm, AE = 8 cm and CF = 10 cm, then find CD.
A)
17cm done
clear
B)
12cm done
clear
C)
10cm done
clear
D)
15cm done
clear
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question_answer2)
Parallelograms on the same base and between the same parallels are equal in
A)
Perimeter done
clear
B)
Shape done
clear
C)
Area done
clear
D)
None of these done
clear
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question_answer3)
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)
\[~204\,c{{m}^{2}}\] done
clear
B)
\[~1644\text{ }c{{m}^{2}}\] done
clear
C)
\[~1645\,c{{m}^{2}}\] done
clear
D)
\[~1600\,c{{m}^{2}}\] done
clear
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question_answer4)
The median of a triangle divides it into two
A)
Triangles of equal area done
clear
B)
Congruent triangles done
clear
C)
Right angled triangles done
clear
D)
Isosceles triangles done
clear
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question_answer5)
In the given figure, ABCD is a parallelogram and P is mid-point of AB. If \[(APCD)=36\,c{{m}^{2}},\]then \[ar\,(\Delta ABC)=\]
A)
\[36\text{ }c{{m}^{2}}\] done
clear
B)
\[~48\,c{{m}^{2}}\] done
clear
C)
\[24\text{ }c{{m}^{2}}\] done
clear
D)
None of these done
clear
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question_answer6)
In the given figure, if ABCD is a parallelogram and E is the mid-point of BC, then \[ar\,(\Delta DEC)=k\]\[ar(ABCD).\]Find k.
A)
2 done
clear
B)
\[\frac{1}{4}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{2}{3}\] done
clear
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question_answer7)
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 \[\Delta BED=K\] area of \[\Delta ABC\]. Find K
A)
2 done
clear
B)
\[\frac{1}{4}\] done
clear
C)
4 done
clear
D)
\[\frac{1}{2}\] done
clear
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question_answer8)
In the given figure, if \[ar(\Delta ABC)=28\,\,c{{m}^{2}}\], then \[ar(AEDF)=\]
A)
\[21\text{ }c{{m}^{2}}\] done
clear
B)
\[~18\,c{{m}^{2}}\] done
clear
C)
\[~16\text{ }c{{m}^{2}}\] done
clear
D)
\[~14\text{ }c{{m}^{2}}\] done
clear
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question_answer9)
In the given figure, ABCD is a quadrilateral with BD = 20 cm. If \[AL\bot BD\] and \[CM\bot BD\]such that AL= 10 cm and \[CM=5\,cm.\] find the area of quadrilateral ABCD.
A)
\[~150\text{ }c{{m}^{2}}\] done
clear
B)
\[~180\text{ }c{{m}^{2}}\] done
clear
C)
\[~100\,c{{m}^{2}}\] done
clear
D)
\[~140\,c{{m}^{2}}\] done
clear
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question_answer10)
The mid-points of the sides of \[\Delta ABC\] along with any of the vertices as the fourth point make a parallelogram of area equal to
A)
\[\frac{1}{2}\]area\[(\Delta ABC)\] done
clear
B)
\[\frac{1}{3}\]area\[(\Delta ABC)\] done
clear
C)
\[\frac{1}{4}\]area\[(\Delta ABC)\] done
clear
D)
area \[(\Delta ABC)\] done
clear
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question_answer11)
In the given figure, ABCD is a parallelogram, \[AL\bot BC,\,AM\bot CD,\]\[AL=4cm\]and AM = 5 cm. If BC= 6.5 cm, then find CD.
A)
5.2 cm done
clear
B)
8.7 cm done
clear
C)
6.5 cm done
clear
D)
3.3 cm done
clear
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question_answer12)
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 \[24\text{ }c{{m}^{2}}\] done
clear
B)
A square of area\[25\text{ }c{{m}^{2}}\] done
clear
C)
A trapezium of area\[24\text{ }c{{m}^{2}}\] done
clear
D)
A rectangle of area\[~24\,c{{m}^{2}}\] done
clear
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question_answer13)
ABCD is a rectangle with O as any point in its interior. If \[ar(\Delta AOD)=3c{{m}^{2}}\] and \[ar\,(\Delta BOC)\]\[=6\,c{{m}^{2}},\]then area of rectangle ABCD is
A)
\[~9\,c{{m}^{2}}\] done
clear
B)
\[~12\text{ }c{{m}^{2}}\] done
clear
C)
\[~15\,c{{m}^{2}}\] done
clear
D)
\[~18\,c{{m}^{2}}\] done
clear
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question_answer14)
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)
\[\frac{1}{2}\] done
clear
B)
4 done
clear
C)
3 done
clear
D)
\[\frac{1}{4}\] done
clear
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question_answer15)
E is any point on median AD of \[\Delta ABC.\]If \[ar(\Delta ACE)=10c{{m}^{2}}\] then \[ar\,(\Delta \,ACE)\] is
A)
\[~20\text{ }c{{m}^{2}}\] done
clear
B)
\[~5\text{ }c{{m}^{2}}\] done
clear
C)
\[~30\text{ }c{{m}^{2}}\] done
clear
D)
\[10c{{m}^{2}}\] done
clear
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question_answer16)
Two parallelograms are on same base and between same parallels. Then, the ratio of their areas is
A)
1 : 2 done
clear
B)
1 : 1 done
clear
C)
2 : 1 done
clear
D)
3 : 1 done
clear
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question_answer17)
ABCD is a parallelogram. P is any point on CD. If \[ar(\Delta DPA)=15\,c{{m}^{2}}\]and \[ar(\Delta APC)=20\,c{{m}^{2}},\]then \[ar(\Delta APB)=\]
A)
\[~15\,c{{m}^{2}}\] done
clear
B)
\[~20\,c{{m}^{2}}\] done
clear
C)
\[~35\,c{{m}^{2}}\] done
clear
D)
\[~30\,c{{m}^{2}}\] done
clear
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question_answer18)
If AD is median of \[\Delta ABC\]and P is a point on AC such that \[ar(\Delta ADP):ar(\Delta ABD)=2:3,\]then\[ar(\Delta PDC):\] \[ar(\Delta ABC)\]is
A)
1 : 5 done
clear
B)
5 : 1 done
clear
C)
1 : 6 done
clear
D)
3 : 5 done
clear
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question_answer19)
The area of a trapezium whose parallel sides are 9 cm & 16 cm and the distance between these sides is 8 cm, is
A)
\[~60\text{ }c{{m}^{2}}\] done
clear
B)
\[~72\text{ }c{{m}^{2}}\] done
clear
C)
\[56\,c{{m}^{2}}\] done
clear
D)
\[100c{{m}^{2}}\] done
clear
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question_answer20)
If E, F, G and H are the mid-points of sides of a parallelogram ABCD then \[ar(EFGH)=\_\_\_\_.\]
A)
\[\frac{1}{3}\,ar\,(ABCD)\] done
clear
B)
\[\,ar\,(ABCD)\] done
clear
C)
\[\frac{1}{2}\,ar(ABCD)\] done
clear
D)
\[\frac{1}{4}\,ar(ABCD)\] done
clear
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question_answer21)
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\[ar(\Delta DPX)+ar(\Delta CQX)=kar(ABCD),\]find k.
A)
\[\frac{2}{3}\] done
clear
B)
\[\frac{3}{2}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{1}{3}\] done
clear
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question_answer22)
ABCD is a parallelogram. E is a point on 6C such that BE : EC = m : n. If AE and DB intersect at F, then what is the ratio of the area of AFEB to the area of \[\Delta AFD\]
A)
\[\frac{m}{n}\] done
clear
B)
\[{{\left( \frac{m}{n} \right)}^{2}}\] done
clear
C)
\[{{\left( \frac{n}{m} \right)}^{2}}\] done
clear
D)
\[{{\left( \frac{m}{m+n} \right)}^{2}}\] done
clear
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question_answer23)
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)
D)
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question_answer24)
ABCD is a trapezium with parallel sides AB = a and DC = b. If E and F are mid- points of non-parallel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is
A)
a : b done
clear
B)
\[(a+3b):(3a+b)\] done
clear
C)
\[(3a+b):(a+3b)\] done
clear
D)
\[(2a+b):(3a+b)\] done
clear
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question_answer25)
ABCD is 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) |
\[\frac{1}{6}ar(ABCD)\] |
Q |
\[ar(\Delta EGB)\] |
(ii) |
\[ar(GBCE)\] |
R |
\[ar(\Delta EFC)\] |
(iii) |
\[ar(\Delta GBCE)\] |
S |
\[ar(\Delta EFC)\] |
(iv) |
\[\frac{1}{2}ar(\Delta EBF)\] |
A)
B)
C)
D)
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