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 perimeter and area of rectangles and squares• find circumference and area of circles

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

Circumference: • the distance around the outside of a circle

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

Some Common Formulas

SquarePerimeter: P = 4s

Area: A = s2

RectanglePerimeter: P = 2b + 2h

Area: A = bhb = baseh = height

s = side

Circle

d = diameterr = radius

Circumference: C = d or C = 2r

Area: A = r2

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