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AreaAreas of Parallelograms and Triangles MATHS - AreaAreas of Parallelograms and Triangles

Rajasthan Board (RBSE) - STD 9 - MATHS (Rajasthan - English Medium). 76 questions in this chapter.

Question types

AreaAreas of Parallelograms and Triangles question types

76 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

76
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6
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5
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Sample Questions

AreaAreas of Parallelograms and Triangles questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q1 Mark
Look at the statements given below:
$i.$ A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
$ii.$ In a $\|gm \  \text{ABCD,}$ it is given that $AB = 10\ cm.$ The altitudes $DE$ on $AB$ and $BF$ on $AD$ being $6\ cm$ and $8\ cm$ respectively, then $AD = 7.5\ cm.$
$iii.$ Area of a $\|gm =\frac{1}{2}\times\text{base}\times\text{altitude}.$
Which is true?
  • A
    $I$ only
  • B
    $II$ only
  • ✓
    $I$ and $II$
  • D
    $II$ and $III$

Answer: C.

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Q 2M.C.Q1 Mark
In the given figure ABCD is a trapezium in which AB || DC such that AB = acm and DC = bcm. If E and F are the midpoints of AD and BC respectively. Then, ar(ABFE) : ar(EFCD) = ?
  1. a : b
  2. (a + 3b) : (3a + b)
  3. (3a + b) : (a + 3b)
  4. (2a + b) : (3a + b)
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Q 3M.C.Q1 Mark
If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is:
  1. 1 : 2
  2. 1 : 3
  3. 1 : 4
  4. 3 : 4
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Q 4M.C.Q1 Mark
In the given figure, $\text{ABCD}$ is a $\|gm$ in which diagonals $AC$ and $BD$ intersect at $O$. If $ar ( \|gm\ \text{ABCD)}$ is $52\ cm^2,$ then the ar $(\triangle\text{AOB})=?$
  • A
    $26\ cm^2$
  • B
    $18.5\ cm^2$
  • C
    $39\ cm^2$
  • ✓
    $13\ cm^2$

Answer: D.

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Q 5M.C.Q1 Mark
Which of the following is a false statement?
  1. A median of a triangle divides it into two triangles of equal area.
  2. The diagonals of a ||gm divide it into four triangles of equal area.
  3.  In a $\triangle\text{ABC},$ if E is the midpoint of median AD, then $\text{ar}(\triangle\text{BED})=\frac{1}{4}\text{ar}(\triangle\text{ABC}).$
  1. In a trapezium ABCD, it is given that AB || DC and the diagonals AC and BD intersect at O. Then, $\text{ar}(\triangle\text{AOB})=\text{ar}(\triangle\text{ABC}).$
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Q 112 Marks Questions2 Marks
In the adjoining figure, ABCD is a trapezium in which AB || DC and its diagonals AC and BD intersect at O.
Prove that $\text{ar}(\triangle\text{AOD})=\text{ar}\triangle\text{BOC}.$
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Q 132 Marks Questions2 Marks
In the adjoining figure, ABC and ABD are two triangles on the same base AB. If line segment CD is
bisected by AB at O, show that $\text{ar}(\triangle\text{ABC})=\text{ar}(\triangle\text{ABD}).$
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Q 163 Marks Question3 Marks
In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P.
Prove that $\text{ar}(\triangle\text{ABP})=\text{ar}(\text{quadrilateral ABCD}).$
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Q 193 Marks Question3 Marks
In the adjoining figure, BD || CA, E is the midpoint of CA and $\text{BD}=\frac{1}{2}\text{CA}.$ Prove that $\text{ar}(\triangle\text{ABC})=2\text{ar}(\triangle\text{DBC}).$
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Q 203 Marks Question3 Marks
In the adjoining figure, D and E are respectively the midpoints of sides AB and AC of $\triangle\text{ABC}.$ If PQ || BC and CDP and BEQ are straight lines then prove that$\text{ar}(\triangle\text{ABQ})=\text{ar}(\triangle\text{ACP}).$
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Q 215 Marks Questions5 Marks
P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and DA of ||gm ABCD. Show that PQRS is a parallelogram and also show that
$\text{ar}(||\text{gm PQRS})=\frac{1}{2}\times\text{ar}(||\text{gm ABCD}).$
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Q 225 Marks Questions5 Marks
In a trapezium ABCD, AB || DC, AB = acm, and DC = bcm. If M and N are the midpoints ofthe nonparallel sides, AD and BC respectively then find the ratio of
ar(DCNM) and ar(MNBA).
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Q 235 Marks Questions5 Marks
ABCD is a trapezium in which AB || CD, AB = 16cm and DC = 24cm. If E and F are respectively the midpoints of AD and BC, prove that $\text{ar(ABFE)}=\frac{9}{11}\text{ar(EFCD)}.$
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Q 244 Marks Questions4 Marks
The given figure shows a pentagon ABCDE. EG, drawn parallel to DA, meets BA produced at G, and CF, drawn parallel to DB, meets AB produced at F. Show that:
 $\text{ar}(\text{pentagon ABCDE})=\text{ar}(\triangle\text{DGF}).$
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Q 254 Marks Questions4 Marks
In the adjoining figure, the point D divides the side BC of $\triangle\text{ABC}$ in the ratio m : n. Prove that $\text{ar}(\triangle\text{ABD}):\text{ar}(\triangle\text{ADC})=\text{m}:\text{n}$
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Q 264 Marks Questions4 Marks
BD is one of the diagonals of a quadrilaterl ABCD. If $\text{AL}\perp\text{BD}$ and $\text{CM}\perp\text{BD},$show that
ar(quadrilaterl ABCD) $=\frac{1}{2}\times\text{BD}\times(\text{AL}+\text{CM}).$
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Q 284 Marks Questions4 Marks
The vertex A of $\triangle\text{ABC}$ is joined to a point D on the side BC. The mid-point of AD is E.
Prove that $\text{ar}(\triangle\text{BEC})=\frac{1}{2}\text{ar}(\triangle\text{ABC}).$
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