I want to write the formula that gives the area of a regular polygon with base and no. of angles . See the figure I made [made on Paint Mircosoft]!
We can compose any polygon made of triangles, which always have 2 equal sides (Hexagon has 60-60-60 triangles, but it fits here), and the length of the triangle perpendicular to the base.
We can start to say that the area of the polygon is:
We can express with trigonometry:
We replace this at the first formula:
How can we define ?
Remember that the sides of the regular polygon can be found using the formula , and for this case, it should be , and, now we have the full formula:
Please correct me for any mistake, typo or anything else against the guidelines. Ciao!