GENERIC:
SPECIFIC:
Chat with our AI personalities
The formula for the area of a rectangle is length x breadth. In order to prove this works, work out an area of a rectangle using that formula.
You would have a difficult time finding a formula to prove that statement, for two main reasons: 1). The statement is false. A triangle is never a rhombus. 2). Formulas can describe things, but they can't 'prove' things.
To prove the formula you need to integrate the function y = +sqrt(1 - x2) between the limits x = -1 and x = +1, and then double the result to allow for the area under the x-axis. Better still, use polar coordinates and double integrate rdrdA where r goes from 0 to R, the radius of the circle, and the angle A goes from 0 to 2*pi. The result can be VERIFIED by comparing the area and the radius but that is not proof.
This is impossible to prove, as the square root of 2 is irrational.
You cannot prove it since it is not true for a general quadrilateral.