Question 1209968
<pre>

{{{drawing(400,140,-2,29,-2,14,
line(0,0,27,0),
line(6,12,18,12),
line(0,0,6,12),
line(18,12,27,0),
green(line(6,0,6,12),line(18,0,18,12)),
locate(2.5,0,matrix(1,2,6,cm)),
locate(21,0,matrix(1,2,9,cm)),
locate(10,13.73,matrix(1,2,12,cm)),    
locate(-.3,7,matrix(1,2,10,cm)),
green(locate(6.24,7,matrix(1,2,8,cm)))  


)}}}

There are three parts to this trapezoid, a rectangle in the middle, and two
right triangles on each end.

On the left, we have a special right triangle, a 6-8-10 right triangle,
whose sides are twice a 3-4-5 right triangle.

To calculate the longer leg 8, if you need to, {{{sqrt(10^2-6^2)=sqrt(100-36)=sqrt(64)=matrix(1,2,8,cm)}}} 

So the area of the triangle on the left is

{{{A=expr(1/2)*base*height=expr(1/2)*6*8=matrix(1,2,24,cm^2) }}}

The area of the rectangle in the middle is

{{{Area=length*width=12*8=matrix(1,2,96,cm^2)}}}

The area of the right triangle on the right:

{{{A=expr(1/2)*base*height=expr(1/2)*9*8=matrix(1,2,72,cm^2) }}}

Adding the 3 parts:

{{{matrix(1,2,24,cm^2)+matrix(1,2,96,cm^2)+matrix(1,2,72,cm^2)}}}{{{""=""}}}{{{matrix(1,2,192,cm^2)}}}

Edwin</pre>