Scale Factors Area

Lee wants to use a scale factor of 4 to create a scale copy of this drawing. What are the dimensions of her scaled copy?

• length: 8 in.

  height: 4.5 in.

• length: 8 in.

  height: 6 in.

• length: 0.5 in.

  height: 0.375 in.

• length: 6 in.

  height: 5.5 in.

Answer explanation

Multiply both the length and width of the original image by the scale factor of 4, then multiply the length and width of the scaled copy to get the area of the scaled copy.

What is the area of the rectangle when it is enlarged by a scale factor of 3?

• 283.5 sq. ft.

• 94.5 sq. ft.

• 31.5 sq. ft.

• 34.5 sq. ft.

Answer explanation

One way to get area of a scaled copy is to get the area of the original image, then multiply that area by the square of the scale factor.

A floor plan of Ava's new house has a scale of 1 in.: 12 ft. On the floor plan, Ava's bedroom is 3/4 in. by 7/8 in.

What is the actual area of Ava's bedroom?

• 144 sq. ft.

• 7.875 sq. ft.

• 94.5 sq. ft.

• 12 sq. ft.

Answer explanation

The scale is 1 in.: 12 ft., so the scale factor from the floor plan to her actual room is 12. Get the area of the room on the floor plan, then multiply by the square of 12.

Tim is building a birdhouse. The plans have a scale of 1 inch: 2.5 inches. A rectangular wall of his birdhouse has a drawing length of 2 inches and width of 3 inches. What will the actual area of the wall be?

• 6 sq. in.

• 15 sq. in.

• 37.5 sq. in.

• 22.5 sq. in.

Answer explanation

Find the area of the wall according to the plans. Multiply the area of the wall in the plans by the square of the scale factor to get the area of the wall of the actual birdhouse.

If the scale factor is 5, how times larger will the area of the big square be compared to the smaller square?

• 5

• 20

• 25

If the scale factor is less than one, the new figure will be

• an enlargement

• a reduction

• a scale factor

• bigger

The original area of a rectangle is 35 in². If the rectangle is enlarged by a scale factor of 3, what is the new area?

• 105 in²

• 11.6 in²

• 315 in²

• 210 in²

How many times greater is the area of a trapezoid if its side lengths are increased by a factor of 4?

• 4 times greater

• 64 times greater

• 8 times greater

• 16 times greater

• 162.5

• 78.125

• 40

• 32

The area of a triangle is 9. The scale factor is 6. What is the new area?

• 324

• 54

• 15

• 3