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Areas of Parallelograms and Triangles MATHS - Areas of Parallelograms and Triangles

MP Board (MPBSE) - STD 9 - MATHS (Madhya Pradesh - English Medium). 28 questions in this chapter.

Question types

Areas of Parallelograms and Triangles question types

28 questions across 3 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

28
Questions
3
Question groups
5
Question types
Sample Questions

Areas 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
Write the correct answer of the following: 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 rectangle of area $24 \mathrm{~cm}^2$.
  • B
    A square of area $25 \mathrm{~cm}^2$.
  • C
    A trapezium of area $24 \mathrm{~cm}^2$.
  • ✓
    A rhombus of area $24 \mathrm{~cm}^2$.

Answer: D.

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Q 2M.C.Q1 Mark
Write the correct answer of the following: In Fig. if parallelogram $ABCD$ and rectangle $ABEF$ are of equal area, then: 
  • A
    Perimeter of $ABCD$ = Perimeter of $ABEM$.
  • B
    Perimeter of $ABCD$ < Perimeter of $ABEM$.
  • ✓
    Perimeter of $ABCD$ > Perimeter of $ABEM$.
  • D
    Perimeter of $ABCD$ $=\frac{1}{2}$ (perimeter of $ABEM$).

Answer: C.

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Q 3M.C.Q1 Mark
Write the correct answer of the following: Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is:
  • A
    $1 : 2$
  • ✓
    $1 : 1$
  • C
    $2 : 1$
  • D
    $3 : 1$

Answer: B.

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Q 4M.C.Q1 Mark
Write the correct answer of the following: The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to:
  • ✓
    $\frac{1}{2}\ \text{ar}\ (\text{ABC})$
  • B
    $\frac{1}{3}\ \text{ar}\ (\text{ABC})$
  • C
    $\frac{1}{4}\ \text{ar}$
  • D
    $\text{ar}\ (\text{ABC})$

Answer: A.

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Q 5M.C.Q1 Mark
Write the correct answer of the following: The median of a triangle divides it into two:
  • ✓
    Triangles of equal area.
  • B
    Congruent triangles.
  • C
    Right triangles.
  • D
    Isosceles triangles.

Answer: A.

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Q 6True False[1 Marks ]1 Mark
Write True or False and justify your answer: In the figure, $ABCD$ and $EFGD$ are two parallelograms and $G$ is the mid-point of $CD.$ Then, $\text{ar}(\triangle\text{DPC})=\frac{1}{2}\text{ar}(\text{EFGD}).$ 
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Q 7True False[1 Marks ]1 Mark
Write True or False and justify your answer: $PQRS$ is a rectangle inscribed in a quadrant of a circle of radius $13\ cm$ and $A$ is any point on $PQ.$ If $PS = 5\ cm,$ then ar $(\triangle\text{PAS})= 30\ cm^2$.
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Q 8True False[1 Marks ]1 Mark
Write True or False and justify your answer: $ABC$ and $BDE$ are two equilateral triangles such that $D$ is the mid-point of $BC.$ Then $\text{ar}(\triangle\text{BDE})=\frac{1}{4}\text{ar}(\triangle\text{ABC}).$
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Q 9True False[1 Marks ]1 Mark
Write True or False and justify your answer: $ABCD$ is a parallelogram and $X$ is the mid-point of $AB$. If ar $(AXCD) = 24\ cm^2,$ then ar $(ABC) = 24\ cm^2.$
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Q 114 Marks Questions4 Marks
In Fig. $X$ and $Y$ are the mid-points of $AC$ and $AB$ respectively, $QP || BC$ and $CYQ$ and $BXP$ are straight lines. Prove that $ar\ (ABP) = ar\ (ACQ).$
 
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Q 124 Marks Questions4 Marks
In $\triangle\text{ABC}, D$ is the mid-point of $AB$ and $P$ is any point on $BC.$ If $CQ || PD$ meets $AB$ in $Q ($shown in figure$),$ then prove that $\text{ar}(\triangle\text{BPQ})=\frac{1}{2}\text{ar}(\triangle\text{ABC})$ 
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Q 134 Marks Questions4 Marks
In Fig.$9\ PSDA$ is a parallelogram. Points $Q$ and $R$ are taken on $PS$ such that $PQ = QR = RS$ and $PA || QB || RC.$ Prove that $ar\ (PQE) = ar\ (CFD). $
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