Chapter 10: Perimeter and Area
Introduction
Now that we have explored triangles, quadrilaterals, polygons, and circles, we are going to learn how to find the perimeter and area of each. First we will derive each formula and then apply them to different types of polygons and circles. In addition, we will explore the properties of similar polygons, their perimeters and their areas.
 10.1.
Area and Perimeter of Rectangles
 10.2.
Area of a Parallelogram
 10.3.
Area and Perimeter of Triangles
 10.4.
Area of Composite Shapes
 10.5.
Area and Perimeter of Trapezoids
 10.6.
Area and Perimeter of Rhombuses and Kites
 10.7.
Area and Perimeter of Similar Polygons
 10.8.
Circumference
 10.9.
Arc Length
 10.10.
Area of a Circle
 10.11.
Area of Sectors and Segments
 10.12.
Area of Regular Polygons
Chapter Summary
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 Rectangle
P=2b+2h  Perimeter of a Square:
P=4s  Area of a Square:
A=s2  Congruent Areas Postulate
 Area Addition Postulate
 Area of a Parallelogram:
A=bh .  Area of a Triangle:
A=12bh orA=bh2  Area of a Trapezoid:
A=12h(b1+b2)  Area of a Rhombus:
A=12d1d2  Area of a Kite:
A=12d1d2  Area of Similar Polygons Theorem

π  Circumference:
C=πd orC=2πr  Arc Length
 Arc Length Formula: length of
ABˆ=mABˆ360∘⋅πd ormABˆ360∘⋅2πr  Area of a Circle:
A=πr2  Sector of a Circle
 Area of a Sector:
A=mABˆ360∘⋅πr2  Segment of a Circle
 Perimeter of a Regular Polygon:
P=ns  Apothem
 Area of a Regular Polygon:
A=12asn orA=12aP
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
 kite
 isosceles trapezoid
 Find the area and circumference of a circle with radius 17.
 Find the area and circumference of a circle with diameter 30.
 Two similar rectangles have a scale factor
43 . If the area of the larger rectangle is96 units2 , find the area of the smaller rectangle.
Find the area of the following figures. Round your answers to the nearest hundredth.
 find the shaded area (figure is a rhombus)
Texas Instruments Resources
In the CK12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9695.