Grade 7 · Math

7th grade How scaling changes area worksheet

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How scaling changes area

Grade 7 Math Worksheet

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Milo plans a camping tent pad at the scale 5 cm : 2 m. The pad is 10 cm by 20 cm on the plan. How many square meters is the real pad?
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?
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?
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?
Side 1 | 1.5, area 1 | ? (the picture is not printed to size). Zee builds model window B as a copy of window A, with every side 1.5 times as long. B covers how many times as much area as A?
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?
Side 1 | ?, area 1 | 9 (the picture is not printed to size). Esme cuts a small sail A and a bigger sail B, similar triangles. B covers 9 times as much area as A. What is the scale factor from A to B?
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?
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?
Side 1 | 1.5, area 40 | ? (the picture is not printed to size). Noah sews a doll quilt (A) and a bigger quilt (B), similar rectangles. A covers 40 square inches, and the scale factor from A to B is 1.5. How many square inches does B cover?

7th grade How scaling changes area worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

How scaling changes area. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find a real area from a plan: change the scale to square units first (1 cm stands for 3 m, so 1 cm² stands for 9 m²).
I can say how many times as much area a copy has when every side is a number of times as long (the factor times itself).
I can work back from an area to the scale factor, and keep the units straight when the scale mixes cm and m, or m and km.

Standard: 7.G.A.1 (areas)

Words to know

scale: What 1 cm (or 1 inch) on a plan stands for in real life, like 1 cm : 3 m.

scale factor: How many times as long the real thing is as the plan, in one unit.

area factor: How many times as much area: the scale factor times itself.

square cm (cm²): The area of a square that is 1 cm on each side.

cutout: A part of a rectangle that is not there, like a courtyard in the middle.

Common mistakes

Your child multiplied or divided the area by the scale only once.

Your child gave the number for lengths when the question asked about area.

Your child doubled the factor instead of multiplying it by itself. Try it together: a square with sides 3 times as long covers how many of the small squares?

What to say

Ask: if a room is twice as long and twice as wide, how many times as much floor is there?

Ask: if a square's sides get 3 times as long, how many of the small squares fit inside the big one?

Questions parents ask

What is the most common mistake with how scaling changes area?

Your child multiplied or divided the area by the scale only once.

How can I help my child with how scaling changes area?

Ask: if a room is twice as long and twice as wide, how many times as much floor is there?

Are these 7th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 7 math

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