Finding areas of triangles formed in hexagon with squares on triangle sides

[ritwik06]

Homework Statement

A right angled triangle has 3 squares attached to each side(the measure of each is givn in the figure). a hexagon is thus formed. Find its area.

Homework Equations

none

The Attempt at a Solution

I have found the area of the figure except for the following triangles.
triangle QLP and triangle XYZ
Please help me with these two triangles!

 

[ritwik06]

The figure is here

The figure is here

 

[Tedjn]

It may help to know that you can find the area of a triangle to be:

$$A = \frac{1}{2}ab\sin C$$

 

[symbolipoint]

You want the sum of the areas of four regions:

Two are squares, and two are triangles which together can be repositioned to form a rectangle. a*a, b*b, and two of a*b.

 

[ritwik06]

Thanks, the problem seems solved. Thanks a lot!