Question

Please help! Will give medal and become fan!!

Use the formula for area of a triangle to derive the formula for the area of a regular polygon.

Answer 1

Any particular regular polygon in mind or specified?

Answer 2

If it is your choice I would select a square to derive

Answer 3

That is just what the question says =/

Answer 4

How do I derive a square?

Answer 5

We continue on, area of the above square is equal to the sum of the area of each triangle. In this case x=x, thus the base and height of each triangle are equal. Using the formula for a triangle (as the problem requests) the area of one triangle is: A=1/2 x * x or 1/2 x^2.
for both triangles it is twice that so the area of the square is 1/2 x^2 + 1/2 x^2 = to x^2.
x squared is the area of a square. so we have complied with the request.

Answer 6

You could use a regular hexagon and convert it to triangles and do the same.

Answer 7

It would consist of 6 equilateral triangles, then the area would be 6 times the area of one of those equilateral triangles.