- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# In figure below, $PQRS$ and $ABRS$ are parallelograms and $ \mathrm{X} $ is any point on side $ \mathrm{BR} $. Show that

**(i)** $ \operatorname{ar}(\mathrm{PQRS})=\operatorname{ar}(\mathrm{ABRS}) $

**(ii)** $ \operatorname{ar}(\mathrm{AXS})=\frac{1}{2} \mathrm{ar}(\mathrm{PQRS}) $

"

Given:

$PQRS$ and $ABRS$ are parallelograms and \( \mathrm{X} \) is any point on side \( \mathrm{BR} \).

To do:

We have to show that

(i) \( \operatorname{ar}(\mathrm{PQRS})=\operatorname{ar}(\mathrm{ABRS}) \)

(ii) \( \operatorname{ar}(\mathrm{AXS})=\frac{1}{2} \mathrm{ar}(\mathrm{PQRS}) \)

Solution:

(i) Parallelograms $PQRS$ and $ABRS$ lie on the same base $SR$ and between the same parallels $SR$ and $PB$.

This implies,

$ar(PQRS) = ar (ABRS)$....…(i)

(ii) In parallelogram $ABRS$,

$\triangle AXS$ and parallelogram $ABRS$ lie on the same base $AS$ and between the same parallels $AS$ and $BR$.

This implies,

$ar (\triangle AXS) = \frac{1}{2}$ ar(parallelogram $ABRS$.......…(ii)

From (i) and (ii), we get,

$ar (\triangle AXS) = \frac{1}{2}$ ar (parallelogram $PQRS$)

- Related Questions & Answers
- How to show date and time on the X-axis in Matplotlib?
- How to show a figure that has been closed in Matplotlib?
- How can I show and hide div on mouse click using jQuery?
- Show that the set of all languages that are not recursively enumerable on {a} is not countable?
- What is the correct way of using <br>, <br/>, or <br /> in HTML?
- Change figure size and figure format in Matplotlib
- Group result in MySQL and show on list?
- C++ Program to Show the Duality Transformation of Line and Point
- What is zero figure and why girls are behind to attain this?
- How do I show the same Matplotlib figure several times in a single IPython notebook?
- Plot horizontal and vertical lines passing through a point that is an intersection point of two lines in Matplotlib
- How to hide and show canvas items on Tkinter?
- Difference between Point-to-Point and Multi-point Communication
- How do I show a MySQL warning that just happened?
- How to show multiple images in one figure in Matplotlib?
- Fixed Point and Floating Point Number Representations