How scaling changes area

Answer Key - Grade 7 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Kira draws the school hall on a plan at the scale 2 cm : 5 m. The hall is 4 cm by 6 cm on the plan. How many square meters is the real hall?

   150
2. 2.

   Luz draws a small house at the scale 2 cm : 3 m. The floor is 6 cm by 5 cm on the plan. How many square meters is the real floor?

   67.5
3. 3.

   Noah's library plan has the scale 4 cm : 10 m. The reading room is 3 cm by 2 cm on the plan, with one sleepy beanbag. How many square meters is the real room?

   37.5
4. 4.

   Pia's art room covers 175 square meters. The plan has the scale 2 cm : 5 m. How many square cm does the art room cover on the plan?

   28
5. 5.

   Ren's garden covers 45 square meters. The plan has the scale 2 cm : 3 m. How many square cm does the garden cover on the plan?

   20
6. 6.

   Side 1 | 2.5, area 1 | ? (the picture is not printed to size). Ari's tabletop B is a copy of tabletop A, with every side 2.5 times as long. B covers how many times as much area as A?

   6.25
7. 7.

   Side 1 | 0.4, area 1 | ? (the picture is not printed to size). Bo shrinks poster A onto a flyer B, with every side 0.4 times as long. B covers how many times as much area as A?

   0.16
8. 8.

   Side 1 | ?, area 1 | 16 (the picture is not printed to size). Jun builds a small kite A and a bigger kite B, similar shapes. B covers 16 times as much area as A. What is the scale factor from A to B?

   4
9. 9.

   Side 1 | ?, area 1 | 25 (the picture is not printed to size). Kira prints a small flyer A and a bigger poster B, similar rectangles. B covers 25 times as much area as A. What is the scale factor from A to B?

   5
10. 10.

    Side 1 | 2.5, area 48 | ? (the picture is not printed to size). Milo builds a model window (A) and a bigger window (B), similar rectangles. A covers 48 square inches, and the scale factor from A to B is 2.5. How many square inches does B cover?

    300