Polygon Area Formula Math

Area of a regular polygon formula combine the number of sides n and the measure of one side s with the apothem a to find the area a of any regular polygon. The user cross multiplies corresponding coordinates to find the area encompassing the polygon and subtracts it from the surrounding polygon to find the area of the polygon within. How to use the formula to find the area of any regular polygon.

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It could also be either convex or concave.

Polygon area formula math. When n of sides and s length from center to a corner. Consider one side of the polygon. That area is equal to the area of the grey rectangle in this picture. The apothem of a regular polygon is a line segment from the center of the polygon to the midpoint of one of its sides.

It is called the shoelace formula because of the constant cross multiplying for the coordinates making up the polygon like tying sh. 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. By definition all sides of a regular polygon are equal in length. Area of a polygon.

The formula is based on taking the area to the left of the chosen side all the way to the y axis. The area of a figure is the number of squares required to cover it completely like tiles on a floor. Unlike a regular polygon unless you know the coordinates of the vertices there is no easy formula for the area of an irregular polygon. The area is then given by the formula.

Area 343 4tan π n area 343 4tan 3 14 7 area 178 18 cm 2. Area of a square side times side. Area of an irregular polygon. Each side could be a different length and each interior angle could be different.

Area is measured in square units. A n s a 2. That area is shaded grey in this illustration. The area of any regular polygon is equal to half of the product of the perimeter and the apothem.

Have a look at the most common formulas for working with polygons. Area of regular polygon where p is the perimeter and a is the apothem. Most require a certain knowledge of trigonometry not covered in this volume but see trigonometry overview. Computer algorithm for finding the area of any polygon first number the vertices in order going either clockwise or counter clockwise starting at any vertex.

Given the length of a side. The side length s is 7 0 cm and n is the 7 because heptagon has 7 sides the area can be determined by using the formula below. If you know the length of one of the sides the area is given by the formula. The shoelace formula or shoelace algorithm is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their cartesian coordinates in the plane.

Coordinate geometry a method for finding the area of any polygon when the coordinates of its vertices are known. Regular polygon 1 2 n sin 360 n s 2.