Free worksheets with worked answers
Eighteen original problems move from simple scale statements to unit conversion, changing scale and area. Every question includes explicit labels; every answer shows the calculation.
A three-page student pack and a separate three-page worked-answer pack. Download only the student file first if you want to solve without seeing the answers.
SC01–SC06: six rectangles with a direct “1 cm represents … m” scale. Find the actual width and height.
SC07–SC12: convert metres and centimetres, work with ratios, and use inch-to-foot scale statements.
SC13–SC18: calculate rectangle and triangle areas, change a drawing scale, and square a length factor.
SC07 / Drawing length
Convert to one unit before applying the ratio.
The drawing line is 4 cm. Reversing the check gives 4 × 200 = 800 cm, the original actual length.
SC11 / Inch-to-foot scale
At 1/4 inch to 1 foot, divide the drawing length by the number of inches used for one foot.
The statement is not 1:4. In matching units, 0.25 in : 12 in simplifies to 1:48.
SC18 / Area factor
Two independent lengths grow by the same factor.
Multiplying the area by 3 would apply the length factor only once. The new area is 108 cm².
For a ratio such as 1:75, one drawing unit represents 75 of the same real-world unit. For an inch-to-foot statement, retain the units on both sides.
Actual to drawing: divide by the ratio denominator. Drawing to actual: multiply. For a stated number of inches per foot, multiply feet to get drawing inches, or divide drawing inches to get feet.
A result in centimetres is not yet a result in metres. Convert explicitly so the final unit matches the question.
Length uses a linear factor. Area uses its square. A triangle still needs half the base times height after the side lengths are converted.
Use the numbers printed beside each figure. The illustrations are intentionally compact and do not reproduce the stated drawing dimensions. This keeps the task focused on scale reasoning and avoids turning an uncalibrated print into the answer.
For a physical layout exercise with real grid dimensions, use the quarter-inch room worksheet. Its 12 ft × 8 ft room is actually drawn at 1/4 inch to 1 foot in the file.
| Mistake | What goes wrong | A useful check |
|---|---|---|
| Mixing units inside a ratio | Writing 1/4 inch : 1 foot as 1:4 | Convert the foot to 12 inches; the ratio becomes 1:48. |
| Multiplying when you should divide | A reduced drawing becomes larger than the actual object. | At 1:200, a drawing length must be 200 times smaller in matching units. |
| Scaling an area once | A factor of 3 in length is treated as a factor of 3 in area. | Both dimensions change: 3 × 3 = 9. |
A few useful answers
No. The levels describe the calculations in this collection. Beginner uses direct scale statements, intermediate introduces conversions, and challenge adds area and changing scale. Choose by the learner’s current knowledge.
No. Every problem says to use the labels. These diagrams are illustrations, not full-size measuring figures. A separate graph-paper exercise is available for physical measurement.
No. The student pack has three question pages. The separate answer pack has three pages of worked solutions, with matching problem IDs SC01 through SC18.
Yes. Single-page SVGs are included. Keep attribution, link to CC BY 4.0 and say what you changed. If you change the numbers, recalculate the answer before sharing.
