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
PQRS is a parallelogram and A and B are any points on PQ and QR. If \(ar(\parallel ;PQRS) = 48\;c{m^2},\) then \(ar(\triangle PBS) + ar(\triangle ASR)\) is equal to
Question 1 figure 1
  • A
    \(48\;c{m^2}.\)
    Correct
  • B
    \(36\;c{m^2}.\)
  • C
    \(96\,c{m^2}.\;\)
  • D
    \(24\;c{m^2}.\;\)
2
A, B, C, D are mid-points of sides of parallelogram PQRS. If \(ar\;(PQRS) = 36\;c{m^2},\) then ar (ABCD) is
Question 2 figure 1
  • A
    \(18\;c{m^2}.\;\)
    Correct
  • B
    \(30\;c{m^2}.\;\)
  • C
    \(24\;c{m^2}.\;\)
  • D
    \(36\;c{m^2}.\)
3
ABCD is a trapezium in which \(AB\parallel DC\).If \(ar(\triangle ABD) = 24\;c{m^2}\)and AB = 8 cm, then the height of \(\triangle ABC\) is
Question 3 figure 1
  • A
    3 cm.
  • B
    8 cm.
  • C
    4 cm.
  • D
    6 cm.
    Correct
4
In the given figure if \(ar(\parallel ABCD) = 29\;c{m^2}\) and AB = 5.8 cm, then the height of \(\parallel \;ABEF\) is
Question 4 figure 1
  • A
    6 cm.
  • B
    5 cm.
    Correct
  • C
    5.8 cm.
  • D
    4.8 cm.
5
\(AP\parallel BQ\parallel CR\). If \(ar(\triangle AQC) = 17\;c{m^2},\) then \(ar(\triangle PBR)\) is
Question 5 figure 1
  • A
    \(25.5\;c{m^2}.\)
  • B
    \(8.5\;c{m^2}.\)
  • C
    \(34\;c{m^2}.\;\)
  • D
    \(17\,c{m^2}.\)
    Correct
6
In the given figure, ABCD is a parallelogram. If \(ar(\triangle BAP) = 10\;c{m^2}\) and\(ar(\triangle CPD) = 30\,c{m^2},\)then \(ar(\parallel \;ABCD)\)is
Question 6 figure 1
  • A
    \(80\;c{m^2}.\)
    Correct
  • B
    \(100\;c{m^2}.\)
  • C
    \(40\;c{m^2}.\)
  • D
    \(60\,\;c{m^2}.\)
7
ABCD is a square. P and Q are mid-point of AB and DC respectively. If AB = 8 cm, then \(ar\;(\triangle BPD)\) is
Question 7 figure 1
  • A
    \(32\;c{m^2}.\)
  • B
    \(18c{m^2}.\)
  • C
    \(16\;c{m^2}.\)
    Correct
  • D
    \(24\;c{m^2}.\)
8
PQRS is a parallelogram. If X and Y are mid-points of PQ and SR and diagonal SQ is joined, then \(ar(\parallel \;XQRY):ar(\triangle QSR)\) is equal to
Question 8 figure 1
  • A
    it is 1 : 4.
  • B
    it is 1 : 1.
    Correct
  • C
    it is 1 : 2.
  • D
    it is 2 : 1.
9
ABCD and ABEF are parallelograms. M is any point of EB. If \(ar(\parallel \;ABCD) = 28\;c{m^2},\)then \(ar(\triangle FAM)\) is
Question 9 figure 1
  • A
    \(7\;c{m^2}.\)
  • B
    \(21\;c{m^2}.\)
  • C
    \(14\;c{m^2}.\)
    Correct
  • D
    \(28\;c{m^2}.\)
10
ABCD is a parallelogram. Through A a line AEF is drawn to meet DC produced at F. If \(ar(\triangle DCE) = 13\;sq\) units then \(ar\;(\triangle BEF)\) is
Question 10 figure 1
  • A
    6.5 sq units.
  • B
    13 sq. units.
    Correct
  • C
    26 sq units.
  • D
    19.5 sq units.
11
PQR is a triangle. S is any point on a line through P parallel to QR. If T is any point on a line through R parallel to SQ, then the three triangles equal in area are
Question 11 figure 1
  • A
    \(\triangle PQR,\;\triangle QSR,\;\triangle QST.\)
    Correct
  • B
    \(\triangle PQR,\;\triangle QSR,\;\triangle QRT.\)
  • C
    \(\;\triangle QRT,\;\triangle SRT,\;\triangle QSR.\)
  • D
    \(\triangle QSR,\;\triangle TSR,\;\triangle PQR.\)
12
ABCD is a trapezium with parallel sides AB = a cm and DC = b cm. E and F are the mid-points of the non-parallel sides. The ratio of ar (ABFE) to ar (EFCD) is
Question 12 figure 1
  • A
    a : b
  • B
    (3a + b) : (a + 3b).
    Correct
  • C
    (a + 3b) : (3a + b).
  • D
    (2a + b) : (3a + b).
13
In quadrilateral PQRS, M is the mid-point of PR. If ar (SMQR) is \(18\;c{m^2},\) then ar (PQMS) is
Question 13 figure 1
  • A
    \(12\;c{m^2}.\;\)
  • B
    \(36\;c{m^2}.\)
  • C
    \(24\,c{m^2}.\)
  • D
    \(18\;c{m^2}.\)
    Correct
14
ABCD is a parallelogram formed by drawing lines parallel to diagonals of quadrilateral PQRS through its vertices. If \(ar\;(quad\;PQRS) = 15\;c{m^2},\;then\;ar\;(\parallel ABCD)\)is
Question 14 figure 1
  • A
    \(40\,c{m^2}.\)
  • B
    \(25\;c{m^2}.\;\)
  • C
    \(30\;c{m^2}.\)
    Correct
  • D
    \(40\;c{m^2}.\)
15
ABCD is a rectangle with O as any point in its interior. If \(ar\;(\triangle AOD) = 3\;c{m^2}\) \(\;and\;ar\;(\triangle BOC) = 6\;c{m^2},\) \(then\;ar\;(rect\;ABCD)\) is
Question 15 figure 1
  • A
    \(9\;c{m^2}.\)
  • B
    \(12\;c{m^2}.\)
  • C
    \(15\;c{m^2}.\)
  • D
    \(18\;c{m^2}.\)
    Correct