Area of a circle to eight sides and so on. For a polygon with 2"n" sides, the parallelogram will have a base of length "ns", and a height "h". As the number of sides increases, the length of the parallelogram base approaches half the circle circumference, and its height approaches the circle radius. In the limit, the parallelogram becomes a rectangle with width "r" and height "r". There are various equivalent definitions of the constant π. The conventional definition in pre-calculus geometry is the ratio of the circumference of a circle to its diameter: However, because the circumference of a circle is not a
Distance from a point to a line are vertical lines). Corresponding sides of these triangles are in the same ratio, so: If point "S" has coordinates ("x","m") then |"PS"| = |"y" - "m"| and the distance from "P" to the line is: Since "S" is on the line, we can find the value of m, and finally obtain: A variation of this proof is to place V at P and compute the area of the triangle ∆"UVT" two ways to obtain that formula_17 where D is the altitude of ∆"UVT" drawn to the hypoteneuse of ∆"UVT" from "P". The distance formula can then used to express formula_18,