geometry from mixed algebra

By mixing up the procedures for obtaining the arithmetic mean and geometric mean, you can get the formula for the hypotenuse of a right triangle, and the formula for the area of a triangle.
Each mean is a 2-step process, for given positive real numbers x and y.
arithmetic mean:
1. add the two numbers
2. multiply the answer by 1/2
geometric mean:
1. multiply the two numbers
2. raise the answer to the 1/2 power
So, if we do step 1 of the arithmetic mean and then step 2 of the geometric mean, we get
(x + y)^(1/2), which is the formula for the hypotenuse of a right triangle having legs of lengths x^(1/2) and y^(1/2).
And if we do step 1 of the geometric mean and then step 2 of the arithmetic mean, we get (xy)(1/2), which equals (1/2)xy, which is the formula for the area of a triangle having base x and height y.
keywords: Geometry, Mathematics, outside the box