8-4 Changing Dimensions: Perimeter and Area

Course 2

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

8-4 Changing Dimensions: Perimeter and Area

Warm Up

1. What is the area of a figure made up of a rectangle with length 12 cm and height 4 cm and a parallelogram with length 12 cm and height 6 cm?

2. What is the area of a figure consisting of a triangle sitting on top of a rectangle? The triangle has a base of 12 in. and height of 9 in., and the rectangle has a base of 12 in. and height of 5 in.

120 cm2

114 in2

8-4 Changing Dimensions: Perimeter and Area

Problem of the Day

If sixteen people sit, evenly spaced, in a circle for story time, who sits directly across from person 5?person 13

8-4 Changing Dimensions: Perimeter and Area

MA.7.G.4.1 Determine how changes in dimensions affect the perimeter [and] area…of common geometric figures and apply these relationships to solve problems.

Sunshine State Standards

8-4 Changing Dimensions: Perimeter and Area

Additional Example 1: Comparing Perimeters and Areas

Find how the perimeter and the area of the figure change when its dimensions change.

The original figure is a 4 2 in. rectangle.

The smaller figure is a 2 1 in. rectangle.

Draw a model of the two figures on graph paper. Label the dimensions.

= 1 inch

8-4 Changing Dimensions: Perimeter and Area

Additional Example 1 Continued

Find how the perimeter and the area of the figure change when its dimensions change.

P = 2(l + w)

= 2(4 + 2)

P = 2(l + w).

= 2(2 + 1)

= 2(6) = 12 = 2(3) = 6

The perimeter is 12 in. The perimeter is 6 in.

Use the formula for perimeter of a rectangle.

Substitute for l and w.

Simplify.

8-4 Changing Dimensions: Perimeter and Area

= 4 x 2

= 8

A = lw

The perimeter is divided by 2, and the area is divided by 4.

A = lw

= 2

The area is 8 in2. The area is 2 in2.

Use the formula for area of a rectangle.

Substitute for l and w.

= 2 x 1

Simplify.

Additional Example 1 Continued

Find how the perimeter and the area of the figure change when its dimensions change.

8-4 Changing Dimensions: Perimeter and Area

Check It Out: Example 1

Find how the perimeter and area of the figure change when its dimensions change.

When the dimensions of the rectangle are multiplied by 2, the perimeter is multiplied by 2 and the area is multiplied by 4 or 2 .2

8 in.

4 in.

4 in.

2 in.

8-4 Changing Dimensions: Perimeter and Area

Additional Example 2: Application

Draw a rectangle whose dimensions are 4 times as large as the given rectangle. How do the perimeter and area change?

Multiply each dimension by 4.

P = 10 cm

A = 6 cm2

P = 40 cm

A = 96 cm2 When the dimensions of the rectangle are multiplied by 4, the perimeter is multiplied by 4, and the area is multiplied by 16, or 42.

3 cm2 cm

8 cm

12 cm

8-4 Changing Dimensions: Perimeter and Area

Check It Out: Example 2

Draw a rectangle whose dimensions are 2 times as large as the given rectangle. How do the perimeter and area change?

5 cm3 cm

6 cm

10 cm

8-4 Changing Dimensions: Perimeter and Area

Check It Out: Example 2 Continued

2

When the dimensions of the rectangle are multiplied by 2, the perimeter is multiplied by 2, and the area is multiplied by 4, or 2 .

8-4 Changing Dimensions: Perimeter and Area

Additional Example 3: Application

Mei works at a local diner whose speciality is making pancakes. She makes silver dollar pancakes with a diameter of 2 inches as well as regular pancakes with a diameter double that of the silver dollar pancakes. Does a regular pancake have twice the area of a silver dollar pancake? Explain. Use 3.14 for .

Find the area of each pancake and compare.

Silver: A = r2 Regular: A = r2Use the formula.

A (1)2 A (2)2Substitute for r.

A 1 A 4Evaluate the power.A 3.14 A 12.56Multiply.

8-4 Changing Dimensions: Perimeter and Area

Additional Example 3 Continued

Mei works at a local diner whose speciality is making pancakes. She makes silver dollar pancakes with a diameter of 2 inches as well as regular pancakes with a diameter double that of the silver dollar pancakes. Does a regular pancake have twice the area of a silver dollar pancake? Explain. Use 3.14 for .

The area of the silver dollar pancake is 3.14 in2, and the area of the regular pancake is 12.56 in2. When the diameter is doubled, the area is 22, or 4, times as great.

8-4 Changing Dimensions: Perimeter and Area

Check It Out: Example 3

Rae is designing a can for a new line of soup products. The original can had a base diameter of 7 cm and her new design will be double that of the original base diameter. Will the new soup can take up double the shelf space of the original can? Explain. Use 3.14 for .

original can base ≈ 38.47 cmnew can base ≈ 153.86 cmNo, the can will take 2 , or four times the shelf space.

2

2

2

8-4 Changing Dimensions: Perimeter and Area

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

8-4 Changing Dimensions: Perimeter and Area

Lesson Quiz

Find how the perimeter and area of the triangle change when its dimensions change.

The perimeter is multiplied by 2, and the area is multiplied by 4; perimeter = 24, area = 24; perimeter = 48, area = 96.

8-4 Changing Dimensions: Perimeter and Area

1. Identify how the perimeter and area of the triangle change when its dimensions change.

A. the perimeter is multiplied by 2, and the area is multiplied by 4; perimeter 30, area = 30; perimeter 60, area = 120. B. the perimeter is multiplied by 2, and the area is multiplied by 4; perimeter 30, area = 60; perimeter 60, area = 120.

Lesson Quiz for Student Response Systems