NCERT Solutions for Class 9 Maths chapter 9 Exercise 9.2 – Areas of Parallelograms and Triangles
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Here we have listed Class 9 maths chapter 9 exercise 9.2 solutions in PDF that is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

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### Download The PDF of NCERT Solutions for Class 9 Maths chapter 9 Exercise 9.2 “Areas of Parallelograms and Triangles”

Q1. In fig, $\mathrm{ABCD}$ is a parallelogram, $\mathrm{AE} \perp \mathrm{DC}$ and $\mathrm{CF} \perp \mathrm{AD}$. If $\mathrm{AB}=16 \mathrm{~cm}, \mathrm{AE}=8 \mathrm{~cm}$ and $\mathrm{CF}=10 \mathrm{~cm}$, find $\mathrm{AD}$.

Q2. If $\mathrm{E}, \mathrm{F}, \mathrm{G}$ and $\mathrm{H}$ are respectively the mid-points of the sides of a parallelogram $\mathrm{ABCD}$, show that ar (EFGH) $=\frac{1}{2}$ ar $(\mathrm{ABCD})$.

Q3. $\mathrm{P}$ and $\mathrm{Q}$ are any two points lying on the sides $\mathrm{DC}$ and $\mathrm{AD}$ respectively of a parallelogram $\mathrm{ABCD}$. Show that ar $(\mathrm{APB})=\operatorname{ar}(\mathrm{BQC})$.

Q4. In figure, $\mathrm{P}$ is point in interior of a parallelogram $\mathrm{ABCD}$. Show that:
(i) ar ( $\triangle \mathrm{APB})+\operatorname{ar}(\triangle \mathrm{PCD})$
$=\frac{1}{2} \operatorname{ar}\left(\|^{\mathrm{gm}} \mathrm{ABCD}\right)$
(ii) ar ( $\triangle \mathrm{APD})+$ ar $(\Delta \mathrm{PBC})$
$=\operatorname{ar}(\Delta \mathrm{APB})+\operatorname{ar}(\Delta \mathrm{PCD})$

Q5. In fig, PQRS and ABRS are parallelograms and $\mathrm{X}$ is any point on side BR. Show that:
(i) $\operatorname{ar}(\mathrm{PQRS})=\operatorname{ar}(\mathrm{ABRS})$
(ii) $\operatorname{ar}(\mathrm{AX} \mathrm{S})=\frac{1}{2}$ ar $(\mathrm{PQRS})$

Q6. A farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points $\mathrm{P}$ and $\mathrm{Q} .$ In how many parts the fields is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?

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