Question 722681
How to find the area of the shaded region in a triangle if: You know that the triangle is composed of two smaller triangles. And, the first small triangle has the base of 5 and you don't know the height. You just know that the other side of the triangle measures 8. And the second smaller triangle has a base of 4....?
<pre>
{{{drawing(400,3200/11,-6,5,-1,7,locate(-2.5,0,5),locate(2,0,4),
locate(.2,3.1,h), locate(-3,3.4,8), rectangle(-.4,0,0,.4),
line(-5,0,4,0),line(-5,0,0,sqrt(39)),line(0,sqrt(39),4,0),green(line(0,0,0,sqrt(39))) )}}} 

Use the Pythagorean theorem on the right triangle on the left to find h:

 c² = a² + b²
 8² = 5² + h²
 64 = 25 + h²
 39 = h²
&#8730;<span style="text-decoration: overline">39</span> = h

Now that we have the height, we can find the area.
The whole base of the whole big triangle is 5+4 or 9

A = {{{1/2}}}·b·h

A = {{{1/2}}}·9·&#8730;<span style="text-decoration: overline">39</span>

A = 28.10249099  [Round to the number of decimal places your
                  teacher asks you to]

Edwin</pre>