<p>This is probably really easy but I'm drawing a blank here, and not going to miss a chance on learning a shortcut or something..</p>
<p>Right triangle with hypotenuse 9...and other angles are 45 (45-45-90 triangle). What is the area of the triangle?</p>
<p>let the sides be –> a
1/2a*a = area</p>
<p>then use pythagorean theorem:
a^2 + a^2 = 9^2
2a^2 = 81
a^2 = 81/2</p>
<p>1/2a^2 = 81/4
The shortcut in the process is to not solve for a and realize that a^2 is all you need</p>
<p>Or cut the hypot in half perpendicularly to make two smaller right triangles, each with base and height both equal to 9/2. So the total area is 2 x (1/2) x (9/2) x (9/2)</p>
<p>Same answer, no pythag thm at all.</p>
<p>Or 9/sqrt(2) is one of the legs.</p>
<p>
That’s a really clever way to do it.</p>
<p>
It works, but I doubt OP remembers side-side-hyp is a-a-sqrt(2)*a</p>