Search results
Results from the WOW.Com Content Network
The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
It is also the minimum distance between any side of the polygon and its center. This property can also be used to easily derive the formula for the area of a circle, because as the number of sides approaches infinity, the regular polygon's area approaches the area of the inscribed circle of radius r = a.
All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. Together with the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is
The lengths of the sides of a polygon do not in general determine its area. [9] However, if the polygon is simple and cyclic then the sides do determine the area. [10] Of all n-gons with given side lengths, the one with the largest area is cyclic. Of all n-gons with a given perimeter, the one with the largest area is regular (and therefore ...
The area within a circle is equal to the radius multiplied by half the circumference, or A = r x C /2 = r x r x π.. Liu Hui argued: "Multiply one side of a hexagon by the radius (of its circumcircle), then multiply this by three, to yield the area of a dodecagon; if we cut a hexagon into a dodecagon, multiply its side by its radius, then again multiply by six, we get the area of a 24-gon; the ...
Shape Area Perimeter/Circumference Meanings of symbols Square: is the length of a side Rectangle (+)is length, is breadth Circle: or : where is the radius and is the diameter ...
The radius of the inscribed circle is the apothem (the shortest distance from the center to the boundary of the regular polygon). For any regular polygon, the relations between the common edge length a, the radius r of the incircle, and the radius R of the circumcircle are: = = .
The circle and the triangle are equal in area. Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle.