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Polygons

Polygons (polygons) are closed plane line segments (polygon segments) consisting of a finite number of segments. A polygon is a plane figure bounded by lines - do my assignment , such as triangle, quadrilateral, pentagon, hexagon, etc.

The number of sides of a polygon is always equal to the number of corners. Polygons are also called n-corners after the number n of their corners.

If the sides of a polygon are all the same length and all the interior angles between adjacent sides are the same size, it is called a regular polygon - math homework solver . Otherwise it is an irregular polygon.

If every connecting line of two vertices of the polygon lies in the interior (as a diagonal) or on the edge (as a side), then the polygon is convex. It has no interior angle greater than 180°.

Otherwise, the n-corner is concave and has at least one interior angle greater than 180°. If two sides intersect, the polygon is called overlapped.

Angle sum in the polygon

A (convex) n-corner can be divided into (n - 2) triangles. For the interior angle sum Sn of any n-corner we get:

Sn=(n-2)⋅180°.

Number of diagonals

From each corner of a polygon, diagonals can be drawn to the (n - 3) non-adjacent vertices - homework help geometry . These are n - (n - 3) connecting lines, but each line was counted twice. For the number d of diagonals in the polygon applies:

dn=1/2⋅n⋅(n-3)

Area of a polygon

The area of each polygon can be calculated by dividing it into partial triangles or other partial figures. Several variants are possible:

It is in fig. (1):A=AABC+ACDA+ADEA+AEFA

It is in fig. (2): A=AABP+ABCSP+ACDS+ARDE+AQREF+AAQF

It is in Fig. (3):

A=AAxFxFA-AFxExEF-AExDxED-AAxBxAB-ABxCxCB-ACxDxDC

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