Areas Of Parallelograms And Triangles CBSE Questions & Answers

Areas Of Parallelograms And Triangles

This is Mathematics Class 09 Areas of Parallelograms and Triangles CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
ABC is a triangle in which D is the mid-point of BC. E and F are mid-points of DC and AE respectively. If \(ar\;(\triangle ABC) = 16\;c{m^2},\) then \(ar\;(\triangle DEF)\) is
Question 1 figure 1
  • A
    \(1\;c{m^2}.\)
  • B
    \(8\;c{m^2}.\)
  • C
    \(2\;c{m^2}.\)
    Correct
  • D
    \(\;4\;c{m^2}.\;\)
2
If AD is median of \(\triangle ABC\) and P is a point on AC such that \(ar\;(\triangle ADP):ar(\triangle ABD)\)=2:3, then \(ar\;(\triangle PDC):ar(\triangle ABC)\) is
Question 2 figure 1
  • A
    it is 2 : 5.
  • B
    it is 1 : 5.
  • C
    it is 3 : 5.
  • D
    it is 1 : 6.
    Correct
3
The altitude of a parallelogram is twice the length of the base and its area is \(1250\;c{m^2}.\) The lengths of the base and the altitude respectively are :
  • A
    35 cm, 70 cm
  • B
    20 cm, 40 cm
  • C
    25 cm, 50 cm
    Correct
  • D
    15 cm, 30 cm
4
ABCD is a parallelogram one of whose diagonals is AC. Then, which of the following is true ?
Question 4 figure 1
  • A
    \(ar\;(\triangle ADC) > ar(\triangle CBA)\)
  • B
    none of these
  • C
    \(ar\;(\triangle ADC) = ar(\triangle CBA)\)
    Correct
  • D
    \(ar\;(\triangle ABC) < ar(\triangle ADC)\)
5
In the figure, ABCD is a parallelogram and EFCD is rectangle. Now which of the following is correct option ?
Question 5 figure 1
  • A
    \(ar\;(\parallel ADCF)\; = \;ar\;(rect.\;EFCD)\)
  • B
    \(ar\;(\parallel ADCF)\; = \;ar\;(rect.\;ABCD)\)
  • C
    none of these.
  • D
    \(ar\;(\parallel ABCD)\; = \;ar\;(rect.\;EFCD)\)
    Correct
6
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\(c{m^2}\)
    Correct
  • B
    a square of area 25 \(c{m^2}\)
  • C
    a trapezium of area 24 \(c{m^2}\)
  • D
    a rectangle of area 24 \(c{m^2}\)
7
In the figure if area of parallelogram ABCD is \(30\;c{m^2},\) then \(ar\;(ADE) + ar(BCE)\)is equal to
Question 7 figure 1
  • A
    \(20\;c{m^2}.\)
  • B
    \(30\;c{m^2}.\;\)
  • C
    \(25\;c{m^2}.\)
  • D
    \(15\;c{m^2}.\)
    Correct
8
In the figure, parallelogram ABEF and rectangle ABCD have the same base AB and equal area. If AB = x, BC = y and BE = z, then :
Question 8 figure 1
  • A
    x + y = x + z
  • B
    x + y < x + z
    Correct
  • C
    2(x + y) > 2(x + z)
  • D
    x + z < x + y
9
In the figure, ABCD is a parallelogram, if area of \(\triangle AEB\) is \(16\;c{m^2},\) then area of \(\triangle BFC\) is :
Question 9 figure 1
  • A
    \(16\;c{m^2}.\)
    Correct
  • B
    \(24\;c{m^2}.\)
  • C
    \(8\,c{m^2}.\)
  • D
    \(32\;c{m^2}.\)
10
In the figure, PQRS and PQLM are parallelograms and X is any point on side QL. The area of \(\triangle PMX\) is equal to :
Question 10 figure 1
  • A
    \(area\;of\;\parallel \;PQRS\)
  • B
    \(area\,of\;\triangle SPM\)
  • C
    \({1 \over 2}\;area\;of\parallel \;gm\;PQLM\)
    Correct
  • D
    \(area\;of\;\triangle RQL\)
11
In the figure, the area of parallelogram ABCD is :
Question 11 figure 1
  • A
    \(AD\, \times DL\)
  • B
    \(AB\; \times BM\)
  • C
    \(DC\; \times DL\)
    Correct
  • D
    \(BC\; \times BN\)
12
In the figure, PQRS is a parallelogram, \(PM \bot RS\) and \(RN \bot PS.\) If PQ = 12 cm, PM = 6 cm and RN = 8 cm, then the length of PS is equal to :
Question 12 figure 1
  • A
    9 cm
    Correct
  • B
    12 cm
  • C
    4 cm
  • D
    18 cm
13
Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between the longer sides is 12 cm, then the distance between the shorter sides is :
  • A
    16 cm
    Correct
  • B
    9 cm
  • C
    18 cm
  • D
    none of these
14
The area of the parallelogram ABCD in the figure is :
Question 14 figure 1
  • A
    \(10\;c{m^2}\)
  • B
    \(15\;c{m^2}\)
  • C
    \(12\,c{m^2}\)
    Correct
  • D
    \(9\;c{m^2}\)
15
If the sum of the parallel sides of a trapezium is 7 cm and distance between them is 4 cm, then area of the trapezium is :
  • A
    \(28\;c{m^2}\)
  • B
    \(7\,c{m^2}\)
  • C
    \(21\;c{m^2}\)
  • D
    \(14\;c{m^2}\)
    Correct