Effects of Dilations on Area

This video lesson focuses on the effects of dilations on two-dimensional shapes, specifically how they impact linear and area measurements. The teacher explains that when a shape is dilated, its area is multiplied by the square of the scale factor, while its perimeter is multiplied by the scale factor itself. The lesson includes example problems and exercises for students to practice these concepts, emphasizing the importance of understanding the relationship between scale factors and the resulting changes in area and perimeter.

What is the main focus of the lesson on dilations?

• Exploring the properties of circles

• Learning about the history of geometry

• Modeling the effect of dilations on linear and area measurements of two-dimensional shapes

• Understanding the effect of dilations on three-dimensional shapes

When a shape is dilated, how is the area affected?

• The area is multiplied by the scale factor

• The area remains unchanged

• The area is multiplied by the scale factor squared

• The area is divided by the scale factor

How is the perimeter of a shape affected by dilation?

• The perimeter is multiplied by the scale factor squared

• The perimeter remains unchanged

• The perimeter is divided by the scale factor

• The perimeter is multiplied by the scale factor

In the example with rectangles ABCD and EFGH, what is the ratio of their perimeters?

• 5:6

• 3:4

• 1:2

• 2:5

What is the ratio of the areas of rectangles ABCD and EFGH?

• 9:16

• 6:37.5

• 4:25

• 1:2

If the dimensions of rectangle ABCD are increased by a factor of 5, what is the area of the enlarged rectangle?

• 150 cm²

• 90 cm²

• 60 cm²

• 30 cm²

A hexagon with an area of 75 square inches is dilated by a scale factor of 3. What is the area of the new hexagon?

• 300 square inches

• 150 square inches

• 675 square inches

• 225 square inches

What should students do after completing problems 16, 22, and 24?

• Submit them online

• Bring them to the teacher for a stamp

• Discuss with a partner

• Move on to the next lesson

Two rectangles are similar with a ratio of 3:4. If the area of the larger is 80, what is the area of the smaller?

• 45

• 60

• 75

• 90

If the perimeter of a smaller pentagon is 24 inches and the scale factor is 1:2, what is the perimeter of the larger pentagon?

• 48 inches

• 24 inches

• 36 inches

• 12 inches