Formula For Polygon Math

If you know the length of one of the sides the area is given by the formula.

Formula for polygon math. A regular polygon has all angles equal and all sides equal otherwise it is irregular. Have a look at the most common formulas for working with polygons. Triangle 3 2 180. The sum of the measures of the interior angles of a convex polygon with n sides is.

Right triangle and pythagora s theorem pythagora s theorem. The area of any regular polygon is equal to half of the product of the perimeter and the apothem. Polygons those many sided objects so popular in geometry circles are subject to their own formulas that help you find the area and angles of various geometrical shapes. If any internal angle is greater than 180 then the polygon is concave.

Area of regular polygon where p is the perimeter and a is the apothem. A table of formulas for geometry related to area and perimeter of triangles rectangles cercles sectors and volume of sphere cone cylinder are presented. N 2 180. The apothem of a regular polygon is a line segment from the center of the polygon to the midpoint of one of its sides.

Given the length of a side. The figure below is not a polygon since it is not made of line segments. The figure below is not a polygon since its sides do not intersect in exactly two places each. The two sides a and b of a right triangle and the hypotenuse c are related by a 2 b 2 c 2.

A polygon that has all its sides equal with equal angles. And there are 2 such triangles per side or 2n for the whole polygon. The total purple area is s a 1 r 4 9 1 1 9 1 2 which can be confirmed by observing that the outer square is partitioned into an infinite number of l shaped areas each with four purple squares and four yellow squares which is half purple. The sum of the angles of a polygon with n sides where n is 3 or more is 180 n 2 degrees.

Area of polygon n radius 2 sin 2 π n area of polygon n side 2 tan π n a table of values. Another geometric series common scale a 4 9 and common ratio r 1 9 shown as areas of purple squares. A convex polygon has no angles pointing inwards. How to use the formula to find the area of any regular polygon.

Polygon formulas n of sides and s length from center to a corner area of a regular polygon 1 2 n sin 360 n s 2. By definition all sides of a regular polygon are equal in length. Sum of the interior angles of a polygon n 2 x 180 the number of diagonals in a polygon 1 2 n n 3 the number of triangles when you draw all the diagonals from one vertex in a polygon n 2 polygon parts.