Section 1-7 Perimeter, Area, Circumference SPI 21B: solve equations to find length, width, perimeter and areaSPI 32L: determine the area of indicated regions involving figuresSPI 41A: determine the perimeter & area of 3 or 4 sided plane figures

Objectives:• Find the area and perimeter of irregular geometric figures• Find the area and perimeter of regular geometric figures• Apply area and perimeter formulas to real world situations• Discover relationships between different geometric figures• Find Volume of rectangular solids

Outline of LessonVocabularyCommon formulas for geometric figuresIrregular geometric figuresVolume of Rectangular Solids

Perimeter: • the sum of the lengths of the sides of a polygon• fence around a plot of land

Circumference: • the distance around the outside of a circle• the distance around the earth

Area:• number of units (squared) enclosed by the perimeter

Amount of carpet needed for a room

• number of units enclosed by the circumference (circle)

Amount of material needed to construct a trampoline

Base: bottom of a figure

Height/Altitude: line perpendicular to base extending to the top of the figure

base

height

Diameter: a straight line connecting the center of a circle with two points on its perimeter

Radius: the length of a line segment between the center and circumference of a circle

Some Common Formulas

SquarePerimeter: P = 4s

Area: A = s2

RectanglePerimeter: P = 2b + 2h

Area: A = bhb = baseh = height

s = side

h

b

Circle

d = diameterr = radius

Circumference: C = d or C = 2r

Area: A = r2

Triangle

b = baseh = height

Perimeter: use the distance formula

Area: A = ½ bh

Some Common Formulas (cont)

Real-World Connection

Fencing. Your pool is depicted in the diagram below. You want to build a fence around the deck. How much fencing will you need?

Width of pool and deck: 15 + 3 + 3 = 21 feet

Length of pool and deck: 20 + 3 + 3 = 26 feet

Solve:P = 2w + 2L Formula = 2(21) + 2(26) Substitute = 94 Simplify

You will need 94 feet of fencing.

Real-World and Finding Circumference

Biology. In the Pacific Northwest, a red fox has a circular home range with a radius of about 718 meters. What is the area of the home range of a red fox?

A = r2 FormulaA = (718) 2 Substitute = 1,619,566 Simplify

Finding Perimeter in the Coordinate Plane

Find the perimeter of ∆ABC.

Find the length of each side.

Side AB. |5 – (-1)| = 6

Side BC. |6- (-2)| = 8

Side AC.

AB + BC + AC = 6 + 8 + 10 = 24. The perimeter is 24 units.

Finding Area of a Rectangle

You are designing a banner for a music festival. The banner will be 4 ft wide by 7 feet high. How much material will you need?

Area of Rectangle = bh

Convert yards to feet: 7 yards = 21 feet

Substitute values into formula

A = 4(21) = 84

You will need 84 square feet (ft2) of material.

Finding Area of Irregular Figures

Find the area of the figure.

Separate the figure into rectangles.

Use Area of a Rectangle Formula

A1 = 6 ∙ 2 = 12

A2 = 4 ∙ 2 = 8

A3 = 2 ∙ 2 = 4

Total Area = 12 + 8 + 4 = 24 cm2

Estimate the area of an Irregular Geometric Figure

• Count the number of square units, by marking the diagram

• Estimate partial units

• Combine partial units to create whole units

• Add the units to estimate area

Finding Area of Irregular Figures

.5

.5

Estimate the Area of the Irregular Geometric Figure

Mark all the whole units 1 1 1

1 1 1

1 1 1

1 1 1

1 1 1 1 1 1

1 1

1 1

1 1Mark the partial units• estimate

1

1

The area is approximately 27 units2

Volume of Rectangular Solids

Volumethe amount of 3-dimensional space occupied by an object

How much product a box of cereal

contains

Volume FormulaV = lwh

Apply Volume Formula of Rectangular Solids

A die is a cube molded from hard plastic.  The edge of a typical die measures 0.62 in.  Dice are usually produced in a mold which holds 100 die at one time.  To the nearest cubic inch, how much plastic is needed to fill this large mold?

V = l · w · h = (.62)(.62)(.62) = .238 in3

For 100 dice = 100 x .238 = 23.8 or approximately 24 cubic inches