Area of Polygons:

Area of a polygon means the polygon itself and its interior.

Postulate: The Area of a Square.

The area of a square is the square of the length of a side.

( A = s²)

Postulate: Area Congruence Postulate.

If two figures are congruent then their areas are equal.

Postulate: Area Addition Postulate.

The area of a region is the sum of the areas of its non-overlapping parts.

Theorem:

The area of a rectangle equals the product of the length of its base and the length of its height.

( A = bh)

Given a a circle, a regular polygon can inscribed in the circle, no matter how many sides the polygon have.

Also, given a regular polygon of any number of sides, a circle can be circumscribed about the regular polygon.

The center of a polygon is also the center of circumscribed circle.

The radius of a regular polygon is the distance from the center to a vertex of the polygon.

The central angle of a regular polygon is the angle formed by two radii drawn from two consecutive vertices.

The apothem of a regular polygon is the perpendicular distance from the center to a side of the polygon.

Theorem:

The area of a regular polygon is equal to the perimeter of the polygon and half the apothem. ( A = ½ ap)