9th Class Mathematics Areas of Parallelograms and Triangles Question Bank

done Areas of Parallelograms and Triangles Total Questions - 50

• question_answer1)
  Two parallelograms are on the same base and between the same parallels. What is the ratio of their areas?
  A)
   2:1                              done clear
  B)
   1:2                  done clear
  C)
   1 :1                 done clear
  D)
     3:1                  done clear
  View Solution play_arrow

• question_answer2)
  ABCD is a parallelogram and 'O' is the point of intersection of its diagonals \[\overline{AC}\] and\[\overline{BD}.\]If the area of\[\Delta AOD=8\,c{{m}^{2}},\] what is the area of the \[\Delta BOC?\]
  A)
  \[2\,c{{m}^{2}}\]                 done clear
  B)
    \[4\,c{{m}^{2}}\]     done clear
  C)
    \[8\,c{{m}^{2}}\]                 done clear
  D)
    \[32\,c{{m}^{2}}\]   done clear
  View Solution play_arrow

• question_answer3)
  The area of a trapezium is \[24\text{ }c{{m}^{2}}.\]The distance between its parallel sides is 4 cm. If one of the parallel sides is 7 cm, what is the measure of the other parallel side?
  A)
   5 cm                           done clear
  B)
   8 cm               done clear
  C)
   12 cm             done clear
  D)
     7 cm               done clear
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• question_answer4)
  The area of a square is\[36\text{ }c{{m}^{2}}.\] If the side of the square is doubled, what is the ratio of area of the original square to that of the new square formed?
  A)
   4 :1                             done clear
  B)
   4 : 3                done clear
  C)
     1:4                  done clear
  D)
     1:2      done clear
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• question_answer5)
  The area of a rhombus is\[60\text{ }c{{m}^{2}}.\]If one of its diagonals is 15 cm, find the other diagonal.
  A)
   4 cm                           done clear
  B)
   8 cm               done clear
  C)
   10 cm             done clear
  D)
     16 cm done clear
  View Solution play_arrow

• question_answer6)
  The area of a triangle is\[16\text{ }c{{m}^{2}}.\] If its base is 8 cm, what is its corresponding altitude?
  A)
   4 cm                           done clear
  B)
   8 cm               done clear
  C)
   18 cm             done clear
  D)
     12 cm             done clear
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• question_answer7)
  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)
  \[32\text{ }c{{m}^{2}}\]                              done clear
  B)
  \[~40\text{ }c{{m}^{2}}\]  done clear
  C)
    \[~26\text{ }c{{m}^{2}}\]              done clear
  D)
    \[28\text{ }c{{m}^{2}}\] done clear
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• question_answer8)
  The ratio of the bases of two triangles is a: b. If the ratio of their corresponding altitudes is c: d, find the ratio of their areas (in the same order).
  A)
   ac: bd                         done clear
  B)
   ad : be done clear
  C)
     bd: ac             done clear
  D)
     be: ad done clear
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• question_answer9)
  The base and corresponding altitude of a parallelogram are 18 cm and 6 cm respectively. What is its area?
  A)
  \[~36\text{ }c{{m}^{2}}\]                          done clear
  B)
  \[~40\text{ }c{{m}^{2}}\]  done clear
  C)
  \[~44\,c{{m}^{2}}\]            done clear
  D)
    \[~108\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer10)
  In\[\Delta ABC,\,AB=8\,cm.\]If the altitudes corresponding to AB and BC are 4 cm and 5 cm respectively, find the measure of BC.
  A)
   6.4 cm                        done clear
  B)
   4.6 cm done clear
  C)
   5.4 cm            done clear
  D)
     4.5 cm done clear
  View Solution play_arrow

• question_answer11)
  ABCD is a trapezium whose area is \[{{a}^{2}}-{{b}^{2}}.\]lf \[AB=a,\,DC=b\]and\[\overline{AB}||\overline{CD},\]what is the distance between the parallel sides?
  A)
   (a - b)                         done clear
  B)
   (a + b)           done clear
  C)
   2(a - b)           done clear
  D)
     2(a + b) done clear
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• question_answer12)
  The diagonals AC and BD of a parallelogram ABCD intersect at O.P is a point on AC such that \[AP=\frac{1}{4}AC.\]Which of the following is true?
  A)
  \[ar(\Delta ADP)=ar(\Delta APB)\] done clear
  B)
  \[ar(\Delta ADP)=ar(\Delta DOC)\] done clear
  C)
   \[ar(\Delta ADP)=ar(\Delta BCD)\] done clear
  D)
  \[ar(\Delta ADP)=ar(\Delta ADB)\] done clear
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• question_answer13)
  In \[\Delta XYZ,P\]and Q are two points on side XZ such that XP = PQ = QZ. Which of the following is correct?
  A)
  \[ar(\Delta PXY)=ar(\Delta PYZ)\] done clear
  B)
  \[ar(\Delta PXY)=ar(\Delta PYQ)=ar(\Delta QYZ)\] done clear
  C)
  \[ar(\Delta PYQ)=ar(\Delta XYQ)\] done clear
  D)
  \[ar(\Delta QYZ)=ar(\Delta XYQ)\] done clear
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• question_answer14)
  A square PQRS and a rhombus RSTU lie on the same base RS. What is the relation between their areas?
  A)
  \[ar(PQRS)=ar(RSTU)\] done clear
  B)
  \[ar(PQRS)<ar(RSTU)\] done clear
  C)
  \[ar(PQRS)>ar(RSTU)\] done clear
  D)
  \[ar(PQRS)=\frac{1}{2}ar(RSTU)\] done clear
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• question_answer15)
  If E, F, G and H are respectively the mid points of the sides of a parallelogram ABCD and ar\[(EFGH)=40c{{m}^{2}},\]find the ar (parallelogram ABCD).
  A)
  \[~40\,c{{m}^{2}}\]                        done clear
  B)
  \[~20\,c{{m}^{2}}\]            done clear
  C)
    \[~80\text{ }c{{m}^{2}}\]              done clear
  D)
    \[~60\text{ }c{{m}^{2}}\] done clear
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• question_answer16)
  If a triangle and a square are on the same base and between the same parallels, What is the ratio of their areas in order?
  A)
   1 : 3                            done clear
  B)
   1 : 2                done clear
  C)
     3 : 1                done clear
  D)
     1 : 4           done clear
  View Solution play_arrow

• question_answer17)
  Direction: Observe the figures given and choose the incorrect statements.
  A)
  \[ar(ABCD)=ar(ADEF)\] done clear
  B)
  \[ar(ABCD)=ar(\Delta ADP)+ar(DEFP)\] done clear
  C)
  \[ar(\Delta ADP)=\frac{1}{2}[ar(ABCD)]\] done clear
  D)
  \[ar(ABCP)=ar(DEFP)\] done clear
  View Solution play_arrow

• question_answer18)
  Direction: Observe the figures given and choose the incorrect statements.
  A)
  \[ar(\Delta APB)=ar(\Delta QCD)\] done clear
  B)
  \[ar(ABQD)=2ar(APQD)\] done clear
  C)
  \[ar(ABQD)=ar(\Delta ABP)+ar(APQD)\] done clear
  D)
  \[ar(ADCP)=ar(\Delta ABP)+ar(APQD)\] done clear
  View Solution play_arrow

• question_answer19)
  Direction: Observe the figures given and choose the incorrect statements.
  A)
  \[ar(ABCD)=ar(PBCS)-ar(PSDA)\] done clear
  B)
  \[ar(ABCD)=ar(AQRD)-ar(QRCB)\] done clear
  C)
  \[ar(ABCD)=ar(PQRS)+[ar(PSDA)-ar(QRCB)]\] done clear
  D)
  \[ar(ABCD)=ar(PQRS)-[ar(PSDA)+ar(QRCB)]\] done clear
  View Solution play_arrow

• question_answer20)
  Direction: Observe the figures given and choose the incorrect statements.
  A)
  \[ar(\Delta BCE)=\frac{1}{2}ar(ABCD)\] done clear
  B)
  \[ar(\Delta BCE)=2ar(ABCD)\] done clear
  C)
  \[ar(\Delta BCE)=ar(ABCD)\] done clear
  D)
  \[ar(\Delta BCE)\] done clear
  View Solution play_arrow

• question_answer21)
  Direction: Based on the figure given, identify the true statements.
  A)
  \[ar(PQRS)=2ar(\Delta PNR)\] done clear
  B)
  \[ar(PQRS)=2ar(MNRS)\] done clear
  C)
  \[ar(PQRS)=ar(MNRS)\] done clear
  D)
  \[ar(MNRS)=2ar(PQRS)\]  done clear
  View Solution play_arrow

• question_answer22)
  Direction: Based on the figure given, identify the true statements.
  A)
  \[ar(\Delta PRS)=ar(\Delta QRN)\] done clear
  B)
  \[ar(\Delta PQR)=ar(\Delta PSR)\] done clear
  C)
  \[ar(\Delta QRN)=\frac{1}{2}ar(PNR)\] done clear
  D)
  \[ar(\Delta PMS)=ar(\Delta QNR)\] done clear
  View Solution play_arrow

• question_answer23)
  In a\[\Delta ABC,G\]is the centroid. What is the ratio of area of \[\Delta AGC\]to area of\[\Delta ABC?\]
  A)
   1 :2                             done clear
  B)
   1 :3                 done clear
  C)
   1:4                  done clear
  D)
     1:6 done clear
  View Solution play_arrow

• question_answer24)
  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                done clear
  B)
   1 : 2    done clear
  C)
     1 : 3    done clear
  D)
                 1 : 4 done clear
  View Solution play_arrow

• question_answer25)
  Find the area of the given quadrilateral ABCD.
  A)
  \[~36\text{ }c{{m}^{2}}\]                          done clear
  B)
  \[~24\text{ }c{{m}^{2}}\]  done clear
  C)
    \[~48\text{ }c{{m}^{2}}\]              done clear
  D)
    \[~32\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer26)
  In the given figure, AB || DC. Identify the triangles that have equal areas.
  A)
  \[\Delta ADX,\Delta ACX\] done clear
  B)
    \[\Delta ADX,\Delta XCB\] done clear
  C)
    \[\Delta ACX,\Delta XDB\]       done clear
  D)
     All the above done clear
  View Solution play_arrow

• question_answer27)
  In the given figure, ABCD is a parallelogram. If area of\[\Delta ABL\]is \[15\text{ }c{{m}^{2}}\]and area of\[\Delta DCL\] is \[32\,c{{m}^{2}},\] find the area of the parallelogram ABCD.
  A)
  \[~94\text{ }c{{m}^{2}}\]  done clear
  B)
                            \[~86\text{ }c{{m}^{2}}\]  done clear
  C)
    \[~72\text{ }c{{m}^{2}}\]              done clear
  D)
    \[~65\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer28)
  Which of the following figures is obtained by joining mid-points of adjacent sides of a rectangle of sides 8 cm and 6 cm?
  A)
   A rectangle of area \[24\,c{{m}^{2}}.\] done clear
  B)
   A square of area \[25\,c{{m}^{2}}.\] done clear
  C)
   A trapezium of area\[24\text{ }c{{m}^{2}}.\] done clear
  D)
   A rhombus of area \[24\text{ }c{{m}^{2}}.\] done clear
  View Solution play_arrow

• question_answer29)
  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 done clear
  B)
   (a + 3b): (3a + b) done clear
  C)
   (1 + 3b): (3a + b) done clear
  D)
   (2a + b): (3a + b) done clear
  View Solution play_arrow

• question_answer30)
  In the given figure, ABCD is a quadrilateral. BP||AC and BP meets DC (pro- duced) in P. If area of the quadrilateral ABCD is 145 square units, find the area of the\[\Delta ADP.\]
  A)
   126 sq. units               done clear
  B)
   145 sq. units   done clear
  C)
     135 sq. units   done clear
  D)
     112 sq. units done clear
  View Solution play_arrow

• question_answer31)
  In the given figure, if p//q, what is the area of \[\Delta ABC?\]
  A)
  \[~77\text{ }c{{m}^{2}}\]                          done clear
  B)
  \[~38.5\text{ }c{{m}^{2}}\]           done clear
  C)
     40 cm             done clear
  D)
    \[~19.25\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer32)
  AD is the median of a\[\Delta ABC\]and the area of \[\Delta ADC=15\,c{{m}^{2}}.\]Find the ar \[(\Delta ABC.)\]
  A)
  \[~15\,c{{m}^{2}}\]                        done clear
  B)
  \[22.5c{{m}^{2}}\]  done clear
  C)
    \[~30\text{ }c{{m}^{2}}\]              done clear
  D)
    \[~37.5\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer33)
  If D, E and F are the mid-points of the sides BC, CA and AB of a \[\Delta ABC\]respectively, what is the quadrilateral AFDE?
  A)
   A square        done clear
  B)
   A rectangle      done clear
  C)
     A parallelogram done clear
  D)
     A trapezium done clear
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• question_answer34)
  A triangle 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                             done clear
  B)
   1 : 2    done clear
  C)
     1 : 3                done clear
  D)
     1 : 4 done clear
  View Solution play_arrow

• question_answer35)
  P is a point in the interior of parallelogram ABCD. If ar \[(I{{I}^{gm}}ABCD)=18c{{m}^{2}},\] what is the value of \[[ar(\Delta APD)+ar(\Delta CPB)]?\]
  A)
  \[~9\,c{{m}^{2}}\]     done clear
  B)
               \[~12\,c{{m}^{2}}\]                        done clear
  C)
  \[~18\,c{{m}^{2}}\]            done clear
  D)
    \[~15\,c{{m}^{2}}\] done clear
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• question_answer36)
  In the given figure, D is the mid-point of BC and L is the mid-point of AD. If ar \[(\ \Delta ABL)=x\]ar \[(\Delta ABC),\] what is the value of\[x?\]
  A)
   2                                 done clear
  B)
   \[\frac{1}{2}\]                        done clear
  C)
  \[\frac{1}{4}\]             done clear
  D)
     4 done clear
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• question_answer37)
  Area of a parallelogram ABCD is \[432\,c{{m}^{2}}.\] 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)
   43.2cm                       done clear
  B)
   10.8cm           done clear
  C)
     18.2cm           done clear
  D)
     21.6cm done clear
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• question_answer38)
  Which of the following statements is true about a median of a triangle?
  A)
   It divides the triangle into two triangles of equal area. done clear
  B)
     It divides the triangle into two congruent triangles. done clear
  C)
     It divides the triangle into two right triangles. done clear
  D)
     It divides the triangle into two isosceles triangles. done clear
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• question_answer39)
  In the given figure, what is the area of parallelogram ABCD?
  A)
  \[~AB\times BM\]        done clear
  B)
    \[~BC\times BN\]                    done clear
  C)
    \[DC\times DL\]                       done clear
  D)
    \[~AD\times DL\] done clear
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• question_answer40)
  In the given figure, S and T are the mid- points of PR and PQ respectively of \[\Delta PQR.\]If ar \[(\Delta PQR)=48c{{m}^{2}},\] find the area of (ATSQ).\[(\Delta TSQ).\]
  A)
  \[48\,c{{m}^{2}}\]                           done clear
  B)
    \[~24\,c{{m}^{2}}\]            done clear
  C)
    \[~12\,c{{m}^{2}}\]                        done clear
  D)
    \[~6\,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer41)
  In\[\Delta ABC,AB=16cm,\,BC=9.6\,cm,\]\[\,CD\bot AB.\]if \[CD=6\,cm,\]find AE.
  A)
   10 cm                         done clear
  B)
     48 cm             done clear
  C)
     8.4 cm                        done clear
  D)
     9.6 cm done clear
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• question_answer42)
  In the given figure, D, E and F are the mid- points of the sides BC, CA and AB respectively of a \[\Delta ABC.\] If ar \[(\Delta DEF)=14c{{m}^{2}},\] find the area of \[\Delta ABC.\]
  A)
  \[~14\,c{{m}^{2}}\]                        done clear
  B)
    \[~28\,c{{m}^{2}}\]                        done clear
  C)
    \[~7\text{ }c{{m}^{2}}\]                            done clear
  D)
    \[~56\text{ }c{{m}^{2}}\] done clear
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• question_answer43)
  In the given figure, REST is a parallelogram. \[TP\bot RE\]and\[TQ\bot ES.\]If TR = 6cm, RE=16 cm and TP = 4.8 cm. what is the length of TQ?
  A)
   12.8 cm                      done clear
  B)
     15 cm             done clear
  C)
     8 cm                           done clear
  D)
     10.2 cm done clear
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• question_answer44)
  In the given figure, ABCD is a parallelogram and L is the mid-point of DC. If ar (ABCL) is \[72\,c{{m}^{2}},\] find ar \[(\Delta ADC).\]
  A)
  \[24\text{ }c{{m}^{2}}\]                              done clear
  B)
    \[~48\text{ }c{{m}^{2}}\]              done clear
  C)
    \[~36c{{m}^{2}}\]                          done clear
  D)
    \[~54c{{m}^{2}}\] done clear
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• question_answer45)
  If In the figure ABCD is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If \[AD=2\sqrt{5}\,cm,\]find the area of the rectangle.
  A)
  \[30\,c{{m}^{2}}\]               done clear
  B)
    \[50\,c{{m}^{2}}\]               done clear
  C)
    \[~40\text{ }c{{m}^{2}}\]                          done clear
  D)
    \[~35\text{ }c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer46)
  In the given figure, D, E and F are the mid-points of the sides BC, CA and AB respectively. If ar \[(BDEF)=x\]ar \[(\Delta AFE),\]what is the value of\[x?\]
  A)
        \[\frac{1}{2}\]                                    done clear
  B)
     1                                 done clear
  C)
                 2                                 done clear
  D)
     4 done clear
  View Solution play_arrow

• question_answer47)
  In the figure given, D divides the side BC of \[\Delta ABC\]in the ratio 3:5. What is the area of\[\Delta ABD?\]
  A)
  \[\frac{2}{5}\times ar(\Delta ABC)\]               done clear
  B)
    \[\frac{3}{5}\times ar(\Delta ABC)\]   done clear
  C)
                 \[\frac{5}{8}\times ar(\Delta ABC)\]  done clear
  D)
                \[\frac{3}{8}\times ar(\Delta ABC)\] done clear
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• question_answer48)
  ABCD is a parallelogram, \[Al\bot CD\]and \[AM\bot BC.\] If AB = 12 cm, AD = 8 cm and AL = 6 cm, find the measure of AM.
  A)
   9 cm                           done clear
  B)
     10 cm done clear
  C)
     12 cm                         done clear
  D)
     15 cm done clear
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• question_answer49)
  ABCD is a parallelogram and P is the midpoint of AB. If ar\[(APCD)=36\,c{{m}^{2}},\]find ar \[(\Delta ABC),\]
  A)
  \[~36\text{ }c{{m}^{2}}\]                          done clear
  B)
    \[~48\text{ }c{{m}^{2}}\]              done clear
  C)
    \[~24\text{ }c{{m}^{2}}\]                          done clear
  D)
    \[~42\text{ }c{{m}^{2}}\] done clear
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• question_answer50)
  In \[\Delta ABC,\, AB =7.2\,cm, BC=4.8cm,\,AM\bot BC\]if \[CL=4\,cm,\]find the measure of AM.
  A)
   12 cm                         done clear
  B)
     8 cm               done clear
  C)
     4 cm                           done clear
  D)
     6 cm done clear
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