Scale Factors and Area Relationships

The video tutorial covers the concept of dilation in geometry, focusing on how scale factors affect the area and perimeter of various shapes, including circles, trapezoids, triangles, polygons, and parallelograms. It also explores the relationship between scale factors and cross-sections of solids, and concludes with an application of trigonometric functions to determine angle measures.

What is the scale factor if a circle's area changes from 8π cm² to 32π cm²?

• 16

• 8

• 4

• 2

If a trapezoid's area increases from 100 to 6400 square units, what is the scale factor?

• 64

• 32

• 16

• 8

How does the perimeter change when a shape is dilated by a scale factor of 3?

• It triples

• It doubles

• It quadruples

• It remains the same

Which graph represents the relationship between scale factor and area?

• Graph C

• Graph A

• Graph B

• Graph D

What is the new area of a polygon with an original area of 10 square units and a scale factor of 4?

• 40

• 200

• 100

• 160

How many times larger is the area of a dilated parallelogram if the scale factor is 2?

• 3 times

• 4 times

• 2 times

• 5 times

Which solid has cross-sections that are dilations of a 2D shape?

• Cylinder

• Cube

• Cone

• Triangular Prism

What is the cosine of angle A if the adjacent side is 28 and the hypotenuse is 53?

• 28/45

• 45/53

• 53/28

• 28/53