Rectangles Are Cool!

Geometry Level 5

In the figure above, $ABCD$ is a rectangle, $PB= 10 \text{ cm}$ , $AS = 8 \text{ cm}$ , $QC=12 \text{ cm}, DR=8 \text{ cm}$ . The area of the triangle $POQ$ and triangle $OSR$ are both $30\text{ cm}^2$ . And $O$ is the intersection point of the straight lines $PR$ and $QS$ . Find the area of the rectangle $ABCD$ (in $\text{m}^2$ ).

Credits to my math teacher for coming up with this problem.

The answer is 0.0238.

5 solutions

Neel Maiti
Nov 28, 2015

The solution is too long for me to write so I have uploaded the pics which show the solution of this problem,I would like someone else to come up with a more simpler and elegant way of the solution to this question. Please be free to ask if you don't understand any part of my approach!