Exploring Dilations and Their Impact on Area and Perimeter

The video tutorial explores how the area and perimeter of figures change when they are dilated. It begins with an introduction to the concept of dilation and its effects on geometric figures. The tutorial provides examples using a rectangle and a square, demonstrating how to calculate the new perimeter and area after dilation. It identifies patterns, showing that the new perimeter is the original perimeter multiplied by the scale factor, while the new area is the original area multiplied by the scale factor squared. The video concludes with practice questions to reinforce these concepts.

What is the perimeter of a rectangle with sides 1 and 3 after a dilation by a scale factor of 2?

• 8

• 16

• 14

• 12

If a square's side is tripled, how many times larger is the new area compared to the original?

• 3 times

• 6 times

• 9 times

• 12 times

How do you find the new perimeter of a dilated figure?

• Original perimeter + scale factor

• Original perimeter / scale factor

• Original perimeter * scale factor squared

• Original perimeter * scale factor

A trapezoid's area becomes 100 times bigger after dilation. What was the scale factor?

• 10

• 20

• 50

• 100

If a parallelogram is dilated by a factor of 0.4, how is the new perimeter related to the original?

• The same as the original perimeter

• 2.5 times the original perimeter

• 0.16 times the original perimeter

• 0.4 times the original perimeter

What is the new area of a figure with an original area of 20 cm² after dilation by a scale factor of 0.5?

• 20 cm²

• 40 cm²

• 10 cm²

• 5 cm²

A figure with a perimeter of 200 is dilated by a scale factor of 3/5. What is the new perimeter?

• 120

• 200

• 80

• 333.33

After dilating a figure with an area of 16 cm² by a scale factor of 4, what is the new area?

• 16 cm²

• 256 cm²

• 64 cm²

• 1024 cm²

Find the new perimeter of a triangle dilated by a scale factor of 3, if the original perimeter was 9 inches.

• 36 inches

• 18 inches

• 12 inches

• 27 inches

What is the new area of a circle dilated by a scale factor of 1/2, if the original area was 12 cm²?

• 12 cm²

• 24 cm²

• 6 cm²

• 3 cm²