Surface Area and Scale Factor Problems

The video tutorial explores the concept of similar shapes and how their areas change with different scale factors. It explains that when the sides of a shape are multiplied by a scale factor, the area is multiplied by the square of that factor. The video provides examples with rectangles and triangles, demonstrating how to calculate the new area after enlargement. It also covers surface area changes and includes exam-style questions to reinforce the concepts.

What is the scale factor of enlargement if a rectangle's side increases from 5 cm to 10 cm?

• 3

• 1

• 4

• 2

If the sides of a shape are multiplied by 3, by what factor does the area increase?

• 6

• 12

• 3

• 9

A triangle has an area of 20 cm² and its base is enlarged by a factor of 3. What is the new area?

• 60 cm²

• 120 cm²

• 180 cm²

• 240 cm²

If a rectangle's sides are enlarged by a factor of 5, how many times larger is the area?

• 15

• 25

• 10

• 5

What is the scale factor of enlargement if the area of a shape increases from 10 cm² to 490 cm²?

• 5

• 7

• 9

• 11

How does the surface area change if the sides of a shape are enlarged by a factor of 2?

• 4 times

• 8 times

• 6 times

• 2 times

What is the area of a parallelogram if its sides are enlarged by a factor of 3 and the larger parallelogram's area is 54 cm²?

• 6 cm²

• 18 cm²

• 12 cm²

• 24 cm²

If the height of a container increases from 24 cm to 36 cm, what is the scale factor of enlargement?

• 1.8

• 1.5

• 2.0

• 1.2

A circle's area is 500 cm², and its diameter is enlarged by a factor of 1.5. What is the new area?

• 1000 cm²

• 1250 cm²

• 750 cm²

• 1125 cm²

If a shape's sides are enlarged by a factor of 4, by what factor does the surface area increase?

• 16

• 12

• 20

• 8