Area and Scale

What is the area of the rectangle when it is reduced by a scale factor of 1/2?

• 28 sq. cm.

• 3.5 sq. cm

• 7 sq. cm.

• 1.75 sq. cm.

Answer explanation

The scale factor is 1/2. The square of the scale factor is 1/4. Get the area of the original image and multiply that area by 1/4.

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.

What is the scale factor from the original image to the scale drawing?

• 2

• 0.5

• 1/4

• 3

Answer explanation

The scaled copy is smaller than the original image so the scale factor from the original image to the scaled copy must be less than one.

What is the scale factor from the original image to the scale drawing?

• 1.5

• 0.6

• 2/3

• 0.4

Answer explanation

The scaled copy is larger than the original image so the scale factor from the original image to the scaled copy must be greater than one.

What is the scale factor of her drawing?

• 10/6

• 2/6

• 3/5

• 1.75

Answer explanation

The scale ratio from the original image to the drawing is written as 6 cm/10 cm. Simplify this ratio and drop the units to get the scale factor. Check the reasonableness of your answer. The scaled copy is smaller than the original image so the scale factor must be less than one.

The scale from the drawing to the actual stop sign is 1 in.: 6 in.

What is the side length of the actual stop sign?

• 11 inches

• 30 inches

• 25 inches

• 12 inches

Answer explanation

To find the scale factor from the drawing to the actual image ask yourself, "What number would I multiply by 1 to get 6?"

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.

What is the area of the rectangle if reduced by a scale factor of 1/8?

• 72 sq. cm.

• 1,152 sq. cm.

• 144 sq. cm.

• 18 sq. cm.

Answer explanation

Multiply the length and width of the original rectangle by the scale factor to get the dimensions of the scaled copy. Multiply the length and width of the scaled copy to find the area.

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.