# Thread: Area - Problem Sum

1. ## Area - Problem Sum

A Villager David has a plot of land of the shape of a quadrilateral. The Village head decided to take over some portion of his plot from one of the corners toconstruct a health center. Suzie Agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this plan can be implemented.

2. Originally Posted by shaurya
A Villager David has a plot of land of the shape of a quadrilateral. The Village head decided to take over some portion of his plot from one of the corners toconstruct a health center. Suzie Agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this plan can be implemented.

Hi,

I've attached a sketch of the transformation.

The rectangle is painted in red, the triangles are painted in blue.

3. Earboth: It's in the shape of a quadrilateral, not a pentagon.

Hint: Try forming a square and splitting it up into four congruent triangles.

4. Can anyone post it using theorums

between the same base and equal parralles.
It would be much easier like that. Earthbot if you can help me.

@ SnipedYou : We cant assume that its a square or a parrallelogram. We just know its a quadrilateral. may it be a trapeizum or watsoever.

5. Originally Posted by shaurya
Can anyone post it using theorums

between the same base and equal parralles.
It would be much easier like that. Earthbot if you can help me.

...
Hi,

I'll try. I've attached a sketch of a quadrilateral ABCD.

1. Draw the diagonal DB
2. Draw a parallel of DB through C
3. This parallel intersect with AB in E
4. The $\displaystyle area \ of\ \Delta DBC = area \ of \ \Delta DBE$ (same base, same height)
5. The area $\displaystyle a(\Delta DFC) = a(\Delta BFE)$
6. Cut off $\displaystyle \Delta DFC$ and glue to the rest the $\displaystyle \Delta FBE$