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
In the given figure ABCD is a parallelogram and its area is \(64\;c{m^2}.\) If P is any point in the interior of \(\parallel \;ABCD,\) then \(ar(\triangle APD) + ar(\triangle PBC)\) is equal to
Question 1 figure 1
  • A
    \(16\,c{m^2}.\)
  • B
    \(48\;c{m^2}.\)
  • C
    \(64\;c{m^2}.\)
  • D
    \(32\;c{m^2}.\;\)
    Correct
2
PQRS is a trapezium with \(PQ\;\parallel \;SR.\) A line parallel to PR intersects PQ at X and QR at Y. If \(ar(\triangle PYR) = 5\;c{m^2},\)then \(ar\;(\triangle PXS)\) is
Question 2 figure 1
  • A
    \(5\;c{m^2}.\)
    Correct
  • B
    \(7.5\;c{m^2}.\)
  • C
    \(10\;c{m^2}.\)
  • D
    \(2.5\;c{m^2}.\)
3
D and E are mid-points of BC and AD respectively. If \(ar\;(\triangle ABC) = 10c{m^2},\) then \(ar\;(\triangle EBC)\) is
Question 3 figure 1
  • A
    \(7.5\;c{m^2}.\)
  • B
    \(5\,c{m^2}.\)
    Correct
  • C
    \(10\;c{m^2}.\)
  • D
    \(2.5\;c{m^2}.\)
4
Points A, B, C, and D are collinear. AB = BC = CD. \(XY\parallel AD.\) If P and M lie on XY and \(ar(\triangle MCD) = 7\;c{m^2},\) then \(ar\;(\triangle APB)\;and\;ar\;(\triangle APD)\) respectively are
Question 4 figure 1
  • A
    \(14\;c{m^2},\,21\;c{m^2}.\)
  • B
    \(7\;c{m^2},\;21\;c{m^2}.\;\)
    Correct
  • C
    \(7\;c{m^2},14\;c{m^2}.\;\)
  • D
    \(\;14\;c{m^2},14\,c{m^2}.\)
5
If E and F are mid-points of sides AB and CD respectively and \(ar(\parallel \;ABCD) = 36\;c{m^2},\;then\;ar\;(APD)\;:\;ar\;(DEF)\)
Question 5 figure 1
  • A
    it is 1 : 1.
  • B
    it is 2 : 1.
    Correct
  • C
    it is 1 : 2.
  • D
    it is 3 : 1.
6
In the given figure, if \(BC\parallel AE,\;CD\parallel BE,\) \(\;and\;ar\;(\triangle BED) = 6\;c{m^2},\) \(then\;ar\;(\triangle ABC)\) is
Question 6 figure 1
  • A
    \(12\;c{m^2}.\)
  • B
    \(8\,c{m^2}.\)
  • C
    \(10\;c{m^2}.\)
  • D
    \(6\;c{m^2}.\)
    Correct
7
In the given figure If \(ar\;(\parallel \;ABEF)\; = \;ar(\parallel \;ABCD) = 50\;c{m^2},\) AFGH is a parallelogram and points E, B, G and H are collinear points, then \(ar\;(\parallel \;AFGH)\) is
Question 7 figure 1
  • A
    \(75\;c{m^2}.\)
  • B
    \(50\;c{m^2}.\)
    Correct
  • C
    \(25\,c{m^2}.\)
  • D
    \(100\;c{m^2}.\)
8
PQRS is a parallelogram. A and B are any points on PQ and RQ respectively. If \(ar\;(\triangle SBR) = 16\;c{m^2}\;and\;ar\;(\triangle PBQ) = 8\;c{m^2},\) then the area of \(\triangle RAS\) is
Question 8 figure 1
  • A
    \(8\;c{m^2}.\)
  • B
    \(16\,c{m^2}.\;\)
  • C
    \(32\,c{m^2}.\)
  • D
    \(24\;c{m^2}.\)
    Correct
9
ABCD is a parallelogram. P is any point on CD. If \(ar\;(\triangle DPA) = 15\;c{m^2}\) and \(ar\;(\triangle APC) = 20\,c{m^2},\) \(then\;ar\;(\triangle APB)\;is\)
  • A
    \(30\;c{m^2}.\)
  • B
    \(15\,c{m^2}.\)
  • C
    \(\;20\;c{m^2}.\)
  • D
    \(35\;c{m^2}.\)
    Correct
10
M and N are the mid-points of sides DC and AB respectively, of a rectangle ABCD. If\(ar\;(rectangle\;ABCD) = 48\;c{m^2},\) then \(ar\;(\triangle EMC)\) is
Question 10 figure 1
  • A
    \(48\;c{m^2}.\;\)
  • B
    \(24\;c{m^2}.\)
  • C
    \(12\,c{m^2}.\)
    Correct
  • D
    \(36\;c{m^2}.\)
11
ABCD is a rectangle in which AB = 8 units and AD = 3 units. If DCEF is a parallelogram, then the area of \(\triangle EFG\) is
Question 11 figure 1
  • A
    24 sq units.
  • B
    16 sq units.
  • C
    12 sq units.
    Correct
  • D
    6 sq units.
12
ABCD is a quadrilateral. A line through D, parallel to AC meets BC produced at E. If \(ar\;(\triangle ABE) = 36\;c{m^2},\) then the ar (quad ABCD) is
Question 12 figure 1
  • A
    \(72\,c{m^2}.\)
  • B
    \(9\;c{m^2}.\)
  • C
    \(18\;c{m^2}.\)
  • D
    \(36\,c{m^2}.\)
    Correct
13
In given figure ABCD and AGEF are parallelograms. If \(ar(\parallel \;AGEF) = 27\;c{m^2},\) then \(ar\;(\triangle ADG) + ar(\triangle GCB)\) is
Question 13 figure 1
  • A
    \(13.5\;c{m^2}.\)
    Correct
  • B
    \(18\,c{m^2}.\)
  • C
    \(27\,c{m^2}.\)
  • D
    \(9\;c{m^2}.\)
14
ABCD is a trapezium in which \(AB\parallel DC.\) A line through A parallel to BC meets diagonal BD at P. If \(ar\;(\triangle BPC) = 5\;c{m^2},\) then \(ar\;(\triangle ABD)\) is
Question 14 figure 1
  • A
    \(7.5\;c{m^2}.\)
  • B
    \(2.5\;c{m^2}.\)
  • C
    \(5\,c{m^2}.\)
    Correct
  • D
    \(10\;c{m^2}.\)
15
PQRS and ADEQ are rectangles. \(RE\parallel AP.\) If \(ar\;(ACPQ) = 25\;c{m^2}\) and \(ar(ABEP) = 10\;c{m^2},\)then ar (PQRS) is
Question 15 figure 1
  • A
    \(35\,c{m^2}.\)
    Correct
  • B
    \(10\,c{m^2}.\)
  • C
    \(25\,c{m^2}.\)
  • D
    \(30c{m^2}.\)