10.12. Area of Regular Polygons http://www.ck12.org
Summary
This chapter covers perimeter and area of all the basic geometric figures. Perimeter and area are compared and
calculated for rectangles, parallelograms, triangles, and then for composite shapes of those figures. The chapter then
branches into perimeter and area for other special geometric figures, namely trapezoids, rhombuses, and kites, as
well as similar polygons. The chapter wraps up with the circumference of circles and arc length followed by the area
of a circle and the area of sectors and segments.
Chapter Keywords
- Perimeter
- Area of a Rectangle:A=bh
- Perimeter of a RectangleP= 2 b+ 2 h
- Perimeter of a Square:P= 4 s
- Area of a Square:A=s^2
- Congruent Areas Postulate
- Area Addition Postulate
- Area of a Parallelogram:A=bh.
- Area of a Triangle:A=^12 bhorA=bh 2
- Area of a Trapezoid:A=^12 h(b 1 +b 2 )
- Area of a Rhombus:A=^12 d 1 d 2
- Area of a Kite:A=^12 d 1 d 2
- Area of Similar Polygons Theorem
- π
- Circumference:C=πdorC= 2 πr
- Arc Length
- Arc Length Formula: length ofAB̂=m 360 AB̂◦·πdorm 360 AB̂◦· 2 πr
- Area of a Circle:A=πr^2
- Sector of a Circle
- Area of a Sector:A=m
AB̂
360 ◦·πr
2 - Segment of a Circle
- Perimeter of a Regular Polygon:P=ns
- Apothem
- Area of a Regular Polygon:A=^12 asnorA=^12 aP
Chapter Review
Find the area and perimeter of the following figures. Round your answers to the nearest hundredth.
- square
- rectangle
- rhombus
- regular pentagon
- parallelogram
- regular dodecagon
Find the area of the following figures. Leave your answers in simplest radical form.
- triangle