Instructions
- Read each scale carefully before calculating.
- Show your multiplication, division, or ratio work.
- Write units in every answer.
- For Problems 5–7, use this definition: scale factor = new figure length ÷ original figure length.
- You may use the hint: if 1 inch represents 4 feet, multiply the drawing length by 4 to find the actual length.
- Complete the problems in order. The questions begin with direct calculations and gradually become more challenging.
Section 1: Find the Actual Length
Use the given scale and drawing measurement to find the actual length.
1. Castle Wall
A castle wall measures 3 1/2 inches on a drawing. The scale is 1 inch = 4 feet. How long is the actual wall?
Work: ____
Answer: __
2. Market Road
A road leading to a medieval market measures 1 1/2 inches on a map. The scale is 1 inch = 8 feet. What is the actual length of the road?
Work: ____
Answer: __
3. Castle Moat
A moat measures 2 1/2 inches on a floor plan. The scale is 1 inch = 8 feet. How wide is the actual moat?
Work: ____
Answer: __
4. Drawbridge
A drawbridge measures 3/4 inch on a plan. The scale is 1 inch = 12 feet. What is the actual length of the drawbridge?
Work: ____
Answer: __
Section 2: Find the Scale Factor
For each pair of similar figures, divide the new measurement by the original measurement. Write the scale factor as a whole number, fraction, or decimal.
5. Enlarged Shield Design
An original shield design has a side length of 6 inches. A larger similar design has a corresponding side length of 9 inches. What is the scale factor from the original design to the larger design?
Work: ____
Answer: __
6. Reduced Map
An original map has a distance of 8 inches between two towns. A smaller similar map shows the same distance as 6 inches. What is the scale factor from the original map to the smaller map?
Work: ____
Answer: __
7. Enlarged Banner
A banner design is 2 1/2 feet long. A similar enlarged banner is 10 feet long. What is the scale factor from the original banner to the enlarged banner?
Work: ____
Answer: __
Section 3: Reproduce a Measurement at a Different Scale
Use the original scale to find the actual measurement first. Then use the new scale to find the measurement for the new drawing.
8. Rebuilding a Castle Wall
A wall is 3 inches long on an old plan with a scale of 1 inch = 8 feet. A new plan will use a scale of 1 inch = 6 feet. How long should the wall be on the new plan?
Work: ____
Answer: __
9. Redrawing a Trade Route
A trade route is 3 inches long on a map with a scale of 1 inch = 4 miles. A new map will use a scale of 1 inch = 3 miles. How long should the route be on the new map?
Work: ____
Answer: __
10. Medieval Castle Floor Plan
A rectangular castle keep is shown on a floor plan. Its drawing length is 4 1/2 inches, and its drawing width is 3 1/4 inches. The original scale is 1 inch = 8 feet.
- Find the actual length and actual width of the keep.
- Find the actual perimeter of the keep.
- A new floor plan will use a scale of 1 inch = 4 feet. Find the length and width of the keep on the new plan.
- Optional challenge: Is the new drawing larger or smaller than the original drawing? Explain why.
Work:
Answer: __
Answer Key
Section 1: Find the Actual Length
1. Castle Wall
3 1/2 × 4 = 14
Answer: 14 feet
2. Market Road
1 1/2 × 8 = 12
Answer: 12 feet
3. Castle Moat
2 1/2 × 8 = 20
Answer: 20 feet
4. Drawbridge
3/4 × 12 = 9
Answer: 9 feet
Section 2: Find the Scale Factor
5. Enlarged Shield Design
Scale factor = new length ÷ original length
9 ÷ 6 = 1 1/2
Answer: 1 1/2
6. Reduced Map
Scale factor = new length ÷ original length
6 ÷ 8 = 3/4
Answer: 3/4
7. Enlarged Banner
Scale factor = new length ÷ original length
10 ÷ 2 1/2 = 4
Answer: 4
Section 3: Reproduce a Measurement at a Different Scale
8. Rebuilding a Castle Wall
Step 1: Find the actual length.
3 × 8 = 24 feet
Step 2: Use the new scale to find the new drawing length.
24 ÷ 6 = 4 inches
Answer: 4 inches
9. Redrawing a Trade Route
Step 1: Find the actual route length.
3 × 4 = 12 miles
Step 2: Use the new scale to find the new drawing length.
12 ÷ 3 = 4 inches
Answer: 4 inches
10. Medieval Castle Floor Plan
Step 1: Find the actual length.
4 1/2 × 8 = 36 feet
Step 2: Find the actual width.
3 1/4 × 8 = 26 feet
Step 3: Find the actual perimeter.
Perimeter = 2 × (length + width)
Perimeter = 2 × (36 + 26)
Perimeter = 2 × 62 = 124 feet
Step 4: Find the length on the new plan.
36 ÷ 4 = 9 inches
Step 5: Find the width on the new plan.
26 ÷ 4 = 6 1/2 inches
Answers:
- Actual length: 36 feet
- Actual width: 26 feet
- Actual perimeter: 124 feet
- New-plan length: 9 inches
- New-plan width: 6 1/2 inches
- Optional challenge: The new drawing is larger because each inch represents fewer feet, so more inches are needed to show the same actual measurement.