Scale Drawings - Practice Worksheets and Assessment (7.G.1) - Free Printable

It looks like you've uploaded a "Scale Drawings Practice Worksheet" with multiple problems related to scale drawings, including:

- Finding missing lengths using scale factors
- Drawing scaled figures
- Determining scale factors
- Calculating areas of scale drawings

Since I can't view images directly, I’ll help you solve the types of problems that appear on this worksheet based on the layout and common math concepts. Let’s go through each section step by step and explain how to solve them.

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🔹 Section 1: Using a Scale to Find a Missing Length

#### Problem 1:
> Greta is on a road trip and is reading a map that has a scale of 1 in : 20 miles. Her trip measures 3.5 inches on the map. What will her actual distance be?

Solution:
- Scale: 1 inch = 20 miles
- Map distance: 3.5 inches
- Actual distance = $ 3.5 \times 20 = 70 $ miles

✔ Answer: 70 miles

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#### Problem 2:
> Jim is building a model airplane. The scale is 1 in : 40 ft. The actual wingspan of the plane is 28 feet. How long will the wings of the model be?

Solution:
- Scale: 1 in → 40 ft
- Actual wingspan = 28 ft
- Model length = $ \frac{28}{40} = 0.7 $ inches

✔ Answer: 0.7 inches

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🔹 Section 2: Reproducing a Scale Drawing

This section asks you to draw shapes using given scale factors.

#### Example: Scale factor = 3
You are given a small grid figure (e.g., a frog or dog), and asked to redraw it 3 times larger.

How to do it:
- Measure each side of the original shape in grid units.
- Multiply each dimension by 3.
- Redraw the shape on a new grid using the new measurements.

💡 Example: If a rectangle is 2 units wide and 1 unit tall, then at scale factor 3, it becomes 6 units wide and 3 units tall.

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#### Example: Scale factor = ½
Now, shrink the shape to half its size.

- Original: 4 units wide → New: $ 4 \times 0.5 = 2 $ units
- Redraw accordingly.

✔ Always label your drawing and show calculations.

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🔹 Section 3: Determining the Scale Factor

For each pair of original and scale drawing, find the scale factor.

#### Problem 1:
Original image: 12.5 cm
Scale drawing: 2.5 cm

Scale factor = $ \frac{\text{Scale drawing}}{\text{Original}} = \frac{2.5}{12.5} = 0.2 $

So, scale factor = 0.2 or 1:5

✔ Answer: 0.2 or 1:5

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#### Problem 2:
Original: 1.75 in
Scale drawing: 2.75 in

Scale factor = $ \frac{2.75}{1.75} = 1.571... \approx 1.57 $

But usually we simplify as a fraction:

$ \frac{2.75}{1.75} = \frac{275}{175} = \frac{11}{7} \approx 1.57 $

✔ Answer: $ \frac{11}{7} $ or ~1.57

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#### Problem 3:
Original: 12 cm
Scale drawing: 9 cm

Scale factor = $ \frac{9}{12} = 0.75 $

✔ Answer: 0.75 or 3:4

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#### Problem 4:
Original: 4 cm
Scale drawing: 2 cm

Scale factor = $ \frac{2}{4} = 0.5 $

✔ Answer: 0.5 or 1:2

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#### Problem 5:
Original: 12 cm
Scale drawing: 6 cm

Scale factor = $ \frac{6}{12} = 0.5 $

✔ Answer: 0.5

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#### Problem 6:
Original: 3 cm
Scale drawing: 9 cm

Scale factor = $ \frac{9}{3} = 3 $

✔ Answer: 3

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🔹 Section 4: Calculating the Area of Scale Drawings

#### Problem 1:
> A scale drawing of a house has a scale of 1 in : 6 feet. The living room has an area of 20 square inches. What is the actual area of the living room?

Step-by-step:

- Scale: 1 in → 6 ft
- But area scales by the square of the scale factor.
- So, scale factor for length = 6
- Scale factor for area = $ 6^2 = 36 $
- Actual area = $ 20 \times 36 = 720 $ square feet

✔ Answer: 720 sq ft

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#### Problem 2:
> Find the area of the shape below when it is increased by a scale factor of 3.

Assume the shape is a rectangle: 8 cm × 32 cm
Area = $ 8 \times 32 = 256 $ cm²

After scaling by 3:
- New dimensions: $ 8×3 = 24 $ cm, $ 32×3 = 96 $ cm
- New area = $ 24 × 96 = 2304 $ cm²

Alternatively:
Area scales by $ 3^2 = 9 $
So, $ 256 × 9 = 2304 $ cm²

✔ Answer: 2304 cm²

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#### Problem 3:
> Brianna made a garden box in her backyard that is 8 feet by 12 feet. She wants to make a scale drawing that is 1/4 the size. Find the area of her new garden.

Original area = $ 8 × 12 = 96 $ sq ft
Scale factor = $ \frac{1}{4} $
Area scale factor = $ \left(\frac{1}{4}\right)^2 = \frac{1}{16} $

New area = $ 96 × \frac{1}{16} = 6 $ sq ft

✔ Answer: 6 sq ft

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#### Problem 4:
> A scale drawing of a rectangular swimming pool has a scale of 1 inch : 4 feet. The width of the pool is 15 inches. What is the actual width?

Scale: 1 in → 4 ft
Drawing width = 15 in
Actual width = $ 15 × 4 = 60 $ feet

✔ Answer: 60 feet

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#### Problem 5:
> Last summer, Brianna planted 2 plants per square foot in her garden box. How many plants will she plant this summer?

Wait — this seems incomplete unless we know the new area.

But from previous problem: new area = 6 sq ft
Plants per sq ft = 2
Total plants = $ 6 × 2 = 12 $

✔ Answer: 12 plants

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#### Problem 6:
> A blueprint of a house has a scale of 1/2 in : 1 foot. Ethan has a playing space that is 10 feet by 5 feet. Would it fit in a space that has dimensions of 3 inches by 2 inches?

Let’s convert actual space to blueprint scale:

Scale: $ \frac{1}{2} $ in = 1 ft → so 1 ft = $ \frac{1}{2} $ in

So:
- 10 ft → $ 10 × \frac{1}{2} = 5 $ inches
- 5 ft → $ 5 × \frac{1}{2} = 2.5 $ inches

Ethan's space on blueprint: 5 in × 2.5 in

Available space: 3 in × 2 in

Compare:
- 5 > 3 → too wide
- 2.5 > 2 → too long

✘ No, it would not fit.

✔ Answer: No, because the required space is 5 in × 2.5 in, which is larger than 3 in × 2 in.

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✔ Summary of Key Concepts

| Concept | Rule |
|--------|------|
| Scale Factor (length) | $ \text{Scale Factor} = \frac{\text{New Size}}{\text{Original Size}} $ |
| Area Scale Factor | $ (\text{Scale Factor})^2 $ |
| Length from Scale | $ \text{Actual} = \text{Map} \times \text{Scale Value} $ |
| Drawing Scaled Shapes | Multiply all sides by scale factor; redraw on grid |

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