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10-4. Comparing Perimeter and Area. Course 1. Warm Up. Problem of the Day. Lesson Presentation. Comparing Perimeter and Area. 10-4. Course 1. Warm Up

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10 4

10-4

Comparing Perimeter and Area

Course 1

Warm Up

Problem of the Day

Lesson Presentation


10 4

Comparing Perimeter and Area

10-4

Course 1

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


10 4

Comparing Perimeter and Area

10-4

Course 1

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


10 4

Comparing Perimeter and Area

10-4

Course 1

Learn to make a model to explore how area and perimeter are affected by changes in the dimensions of a figure.


10 4

Comparing Perimeter and Area

10-4

Course 1

Additional Example 1: Changing Dimensions

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

= 1 inch

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

The original figure is a 4  2 in. rectangle.

The smaller figure is a 2  1 in. rectangle.


10 4

Comparing Perimeter and Area

10-4

P = 2(l + w)

P = 2(l + w).

Course 1

Additional Example 1 Continued

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

Use the formula for perimeter of a rectangle.

Substitute for l and w.

= 2(4 + 2)

= 2(2 + 1)

Simplify.

= 2(6) = 12

= 2(3) = 6

The perimeter is 6 in.

The perimeter is 12 in.


10 4

Comparing Perimeter and Area

10-4

= 4 x 2

A = lw

= 2 x 1

Course 1

Additional Example 1 Continued

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

Use the formula for area of a rectangle.

A = lw

Substitute for l and w.

Simplify.

= 2

= 8

The area is 8 in2.

The area is 2 in2.

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


10 4

Comparing Perimeter and Area

10-4

Course 1

Check It Out: Example 1

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

= 1 inch

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

The original figure is 2 x 2 in. rectangle.

The larger figure is a 4 x 4 in. rectangle.


10 4

Comparing Perimeter and Area

10-4

P = 2(l + w)

P = 2(l + w).

Course 1

Check It Out: Example 1 Continued

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

Use the formula for perimeter of a rectangle.

Substitute for l and w.

= 2(2 + 2)

= 2(4 + 4)

Simplify.

= 2(4) = 8

= 2(8) = 16

The perimeter is 16 in.

The perimeter is 8 in.


10 4

Comparing Perimeter and Area

10-4

= 2 x 2

A = lw

= 4 x 4

Course 1

Check It Out: Example 1 Continued

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

Use the formula for area of a rectangle.

A = lw

Substitute for l and w.

Simplify.

= 16

= 4

The area is 4 in2.

The area is 16 in2.

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


10 4

Comparing Perimeter and Area

10-4

A = 6 cm2

A = 96 cm2

Multiply each dimension by 4.

P = 10 cm

P = 40 cm

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.

Course 1

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?

12 cm

3 cm

8 cm

2 cm


10 4

Comparing Perimeter and Area

10-4

A = 15 cm2

A = 60 cm2

Multiply each dimension by 2.

P = 16 cm

P = 32 cm

When the dimensions of the rectangle are multiplied by 2, the perimeter is multiplied by 2, and the area is multiplied by 4, or 22.

Course 1

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?

10 cm

5 cm

6 cm

3 cm


10 4

Comparing Perimeter and Area

10-4

Course 1

Insert Lesson Title Here

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.


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