How scaling changes area

Answer Key - Grade 7 Math Worksheet - Challenge Me

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

1. 1.

   Ren's model castle has the scale 1 inch : 4 feet. The real castle wall covers how many times as much area as the model wall?

   2304
2. 2.

   Zee measures an island on a map with the scale 1 cm : 500 m. The island is 5 cm by 7 cm on the map. How many square kilometers is the real island?

   8.75
3. 3.

   Ari measures a lake on a map with the scale 1 cm : 400 m. The lake is 5 cm by 6 cm on the map. How many square kilometers is the real lake?

   4.8
4. 4.

   Esme's school plan has the scale 1 cm : 3 m. The building has a square courtyard cut out of its middle, as shown. How many square meters does the real building cover?

   396
5. 5.

   Jun's park plan has the scale 1 cm : 2 m. The lawn has a square pond cut out of it, as shown. How many square meters of real grass is there?

   244
6. 6.

   Kira's playground plan has the scale 1 cm : 5 m. The playground has a square sandpit cut out of it, as shown. How many square meters of real ground is there?

   500
7. 7.

   Noah's library plan uses 1 cm : 3 m, and the room is 7 cm by 8 cm. Noah redraws it at 1 cm : 6 m. How many square cm is the room now?

   14
8. 8.

   Side 1 | ?, area 1 | 1/4 (the picture is not printed to size). Pia copies a big sail A onto a small card B, similar triangles. B covers 1/4 as much area as A. What is the scale factor from A to B?

   1/2
9. 9.

   Side 1 | ?, area 1 | 1/9 (the picture is not printed to size). Ren shrinks a kite design A onto a sticker B, similar shapes. B covers 1/9 as much area as A. What is the scale factor from A to B?

   1/3
10. 10.

    Side 1 | ?, area 1 | 4/9 (the picture is not printed to size). Tala shrinks a poster A onto a flyer B, similar rectangles. B covers 4/9 as much area as A. What is the scale factor from A to B?

    2/3