Section 5.1 Section 5.1 Perimeter and AreaPerimeter and Area

Objective:Objective: Solve problems involving Solve problems involving perimeter and area of triangles and perimeter and area of triangles and rectanglesrectangles

Name __________________Name __________________

NotesNotes

A _____________ is an equation that A _____________ is an equation that shows a relationship among certain shows a relationship among certain quantities.quantities.

Formulas are commonly used in Formulas are commonly used in _________._________.

For examples, the distance around a For examples, the distance around a geometric figure is called the geometric figure is called the ___________.___________.

Key Concept: PerimeterKey Concept: PerimeterRectangle Triangle

Model Model

Words: The perimeter of a rectangles is the sum of twice the length and twice the width

Words: The perimeter of a triangle is the sum of the measures of all three sides.

Symbols: P= 2l + 2w or 2(l + w) Symbols: P = a + b + c

ba

c

w w

l

l

ExampleExample

1. Find the perimeter of the triangle.1. Find the perimeter of the triangle. P = a + b + cP = a + b + c

28.5 cm

12.8 cm

17 cm

ExampleExample

2. Find the perimeter of a rectangle with 2. Find the perimeter of a rectangle with length 15.2 meters and width 10.5 length 15.2 meters and width 10.5 meters.meters.

Find the LengthFind the Length

3. The perimeter of a rectangle is 42 feet. 3. The perimeter of a rectangle is 42 feet. Its width is 10 feet. Find the length.Its width is 10 feet. Find the length.

P= 2l + 2wP= 2l + 2w

ExampleExample

4. The perimeter of a rectangle is 26 4. The perimeter of a rectangle is 26 yards. Its length is 8 yards. Find the yards. Its length is 8 yards. Find the width.width.

Key Concept: AreaKey Concept: Area

Rectangle

Words The area of a rectangle is the product of the length and width

Model

Symbols A = lwSymbols A = lw

w

l

Key Concept: AreaKey Concept: Area

Triangle

Words The area of a triangle is one-half the product of the base and height

Model

Symbols A = 1/2bh h

b

ExampleExample

On your OwnOn your Own

1. The perimeter of a rectangle is 45 1. The perimeter of a rectangle is 45 meters. Its width is 6 meters. What is meters. Its width is 6 meters. What is the length of the rectangle?the length of the rectangle?

On your OwnOn your Own

2. Dena’s mother is making a rectangular 2. Dena’s mother is making a rectangular quilt. She has 117 squares and wants quilt. She has 117 squares and wants the quilt to be nine squares wide. How the quilt to be nine squares wide. How many squares will make up the length of many squares will make up the length of the quilt?the quilt?

H.O.T. ProblemH.O.T. Problem 1. Classify the following statements as true 1. Classify the following statements as true

or false. Explain your reasoning and provide or false. Explain your reasoning and provide examples.examples.

A. The area of a larger rectangle that can be A. The area of a larger rectangle that can be divided into smaller rectangles is the sum of divided into smaller rectangles is the sum of the areas of the smaller rectangles.the areas of the smaller rectangles.

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H.O.T. ProblemH.O.T. Problem

B. The area of a larger rectangle that can B. The area of a larger rectangle that can be divided into smaller rectangles is the be divided into smaller rectangles is the sum of the perimeters of the smaller sum of the perimeters of the smaller rectangles.rectangles.

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Writing in MathWriting in Math

Describe the effect on the perimeter and Describe the effect on the perimeter and area of a rectangle if its length and width area of a rectangle if its length and width are doubled.are doubled.

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