In the figure, $\text{PQR}$ is a straight line. $SQ$ is parallel to $Tp.$ Prove that the quadrilateral $\text{PQST}$ is equal in area to the $\triangle PSR.$
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Areas Theorems on Parallelograms question types
37 questions across 3 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
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Sample Questions
Areas Theorems on Parallelograms questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the given figure, $ST \| PR.$ Prove that: area of quadrilateral $\text{PQRS} =$ area of $\triangle P Q T$.
View full solution →In the given figure area of $\| gm\ \text{PQRS}$ is $30 \ cm ^2$. Find the height of $\| gm\ \text{PQFE}$ if $P Q=6 \ cm$.
View full solution →In the given figure,$ ABC$ is a triangle and $AD$ is the median.
If $E$ is any point on the median $A D$. Show that: Area of $\triangle A B E=$ Area of $\triangle A C E$.
View full solution →If $E$ is any point on the median $A D$. Show that: Area of $\triangle A B E=$ Area of $\triangle A C E$.
Prove that the area of a rhombus is equal to half the rectangle contained by its diagonals.
$\text{ABCD}$ is a quadrilateral in which diagonals $AC$ and $BD$ intersect at a point $O$. Prove that: area $\triangle AOD +$ area $\triangle BOC +$ area $\triangle ABO +$ area $\triangle CDO.$
View full solution →In a parallelogram $\text{PQRS}, T$ is any point on the diagonal $PR$. If the area of $\triangle PTQ$ is $18$ square units find the area of $\triangle PTS.$
View full solution →In the given figure, $\text{ABC}$ is a triangle and $AD$ is the median.
If $E$ is the midpoint of the median $A D$, prove that: Area of $\triangle A B C=4 \times$ Area of $\triangle A B E$
View full solution →If $E$ is the midpoint of the median $A D$, prove that: Area of $\triangle A B C=4 \times$ Area of $\triangle A B E$
$\triangle PQR$ and $\triangle SQR$ are on the same base $QR$ with $P$ and $S$ on opposite sides of line $QR,$ such that area of $\triangle PQR$ is equal to the area of $\triangle SQR$. Show that $QR$ bisects $PS.$
View full solution →In the given figure, $BC\| DE.(a)$ If area of $\triangle ADC$ is $20\ sq$. units, find the area of $\triangle AEB.(b)$ If the area of $\triangle BFD$ is $8$ square units, find the area of $\triangle CEF$
View full solution →In the figure, if the area of $\| gm \text{PQRS}$ is $84 \ cm ^2$; find the area of $(i)\| gm \text{PQMN};(ii)\triangle PQS;(iii)\triangle PQN$
View full solution →In the figure, $\text{ABCD}$ is a parallelogram and $\text{APD}$ is an equilateral triangle of side $80\ cm$, Calculate the area of parallelogram $\text{ABCD}.$
View full solution →In the given figure, $\text{PQRS}$ is a $∥ gm$. A straight line through $P$ cuts $SR$ at point $T$ and $QR$ produced at $N$. Prove that area of $\triangle QTR$ is equal to the area of $\triangle STN.$
View full solution →In the given figure, $A B \| S Q\| D C$ and $A D \| P R \| B C$. If the area of quadrilateral $\text{ABCD}$ is $24$ square units, find the area of quadrilateral $\text{PQRS}.$
View full solution →In a parallelogram $\text{PQRS, M}$ and $N$ are the midpoints of the sides $PQ$ and $PS$ respectively. If area of $\triangle PMN$ is $20$ square units, find the area of the parallelogram $\text{PQRS}.$
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