# Lesson Worksheet: Scale Drawings and Models Mathematics • 7th Grade

In this worksheet, we will practice calculating the scale factor and the dimensions of both the scaled model and the actual object and applying this to real-world problems.

**Q3: **

James is drawing a map to a scale of . If the distance between two cities on the map is 4.5 cm, find the actual distance between them in kilometers.

**Q4: **

A model of a tree is made using a scale of . Find the height of the actual tree if the height of the model is in.

- A ft
- B80 ft
- C ft
- D30 ft

**Q5: **

A picture with width 13 mm and height 37 mm is magnified so that its width becomes 3.25 cm and height becomes cm. Find the value of .

**Q9: **

If the scale factor from a statue to a reduced model for a display is 16 feet to 7 feet, and the height of the original statue is 55 feet, find the height of the model.

- A46 ft
- B ft
- C ft
- D ft
- E ft

**Q10: **

Given a scale drawing, which of the following is equal to the scale?

- A
- B
- C
- D

**Q11: **

At a scary movie opening, a cardboard model of the monster was 9 inches tall. In the movie, the monster’s actual height was 53 feet. What was the scale of the model?

- A
- B
- C
- D
- E

**Q12: **

A scale model of a building is 4.8 inches tall. If 2 inches on the model scale up to 25 feet in reality, determine the actual height of the building.

**Q13: **

A map is scaled such that every in is equivalent to 50 mi. How many miles are represented by 4 inches on the map?

**Q14: **

An insect’s body is 9 centimeters long with 21-centimeter legs. Determine the length of its legs in a model where its body is 3 meters long.

**Q15: **

Jacob drew a map of his school using a scale of 1 inch for every 10 ft. Determine the distance with which the 800 feet between the playground and the boys restroom would be represented on the map.

**Q16: **

Determine the actual area of the given square which is drawn to a scale of 1 cm = 4 km.

**Q18: **

Complete the table.

Drawing Distance | Real Distance | Scale | Magnification or Reduction |
---|---|---|---|

4.2 dm | 30 km |

- A, reduction
- B, magnification
- C, reduction
- D, magnification

**Q19: **

Complete the table.

Drawing Distance | Real Distance | Scale | Magnification or Reduction |
---|---|---|---|

cm | 90 km |

- A70, reduction
- B7, reduction
- C7, magnification
- D70, magnification

**Q20: **

The figure below shows a drawing of the floor plan of a house. The drawing scale is . What is the length and width of the real-life living room?

- A64 m, 36 m
- B6.4 m, 3.6 m
- C12.8 m, 7.2 m
- D16 m, 9 m

**Q21: **

The table below shows some information about a scale drawing. Complete the missing details, including whether the drawing is a magnification or reduction from real life.

The Drawing Distance | The Real Distance | The Scale | Magnification or Reduction |
---|---|---|---|

66 cm | mm |

- A1, magnification
- B3, magnification
- C1, reduction
- D30, magnification
- E30, reduction

**Q22: **

A map is drawn with a drawing scale of . If the actual distance between two cities is 76 km, determine the distance between them on the map.

**Q23: **

A rectangular picture with width 20 mm and height 61 mm is magnified to 4 cm by 12.2 cm. What is the magnification ratio?

- A
- B
- C
- D

**Q24: **

Every inch in a scale model of a car represents ft in reality. If a vehicle is ft long, how long is the scale model?

- A in
- B in
- C9 in
- D in

**Q25: **

Find the scale factor of the smaller parallelogram to the bigger one in the given figure.

- A2
- B
- C
- D3
- E