Ignoring the triangle first off, it is just a parallelogram. We can find the area with:
[tex]A_{P}=b*h=23.8 * 15=357 square ft. [/tex] (see first diagram).
Next, we need to find the area of the triangle. Its a right angle triangle, so the area can be found by:
[tex] A_{T} = \frac{1}{2} wl[/tex]
where w and l are the lengths of the two smaller sides. We have one, and the longer side (hypotenuse) so we can use Pythagoras' Theorem to find the other small side (see second diagram).
[tex]b= \sqrt{ a^{2} - c^{2} } =\sqrt{ 23.8^{2} - 21^{2} }=11.2ft.[/tex]
Then find the area:
[tex] A_{T} =0.5*21*11.2=117.6 square ft.[/tex]
Take the area of the triangle away from the area of the paralellogram:
[tex]357-117.6=239.4 ft^{2} [/tex]
