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.


The distance between two cities on a map is 17 cm and the actual distance between them is 68 km. If the distance between two other cities on the same map is 15 cm, determine the real distance between them.


A line on a drawing is 3 cm long. In real life, the object represented is 57km long. What is the drawing scale?

  • A1 : 190,000
  • B1 : 57,000
  • C1 : 5,700,000
  • D1 : 300
  • E1 : 1,900,000


James is drawing a map to a scale of 110,000,000. If the distance between two cities on the map is 4.5 cm, find the actual distance between them in kilometers.


A model of a tree is made using a scale of 130inft. Find the height of the actual tree if the height of the model is 223 in.

  • A445 ft
  • B80 ft
  • C223 ft
  • D30 ft


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


An engineer makes a model of a 600-meter-tall tower to a scale of 1750:. What is the model’s height in centimeters?


Determine the scale factor for 3=2.7cmm.

  • A13:
  • B190:
  • C19:
  • D12.7:
  • E127:


An apartment’s ceiling is 19 feet high. However, its height on a scale drawing is only 4 inches. Determine the scale of the drawing.

  • A1 inch = 57 feet
  • B1 inch = 2.53 feet
  • C1 inch = 14.25 feet
  • D1 inch = 4.75 feet
  • E1 inch = 0.21 feet


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
  • B767 ft
  • C2255 ft
  • D24116 ft
  • E3716 ft


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

  • Alengthindrawinglengthinreality
  • Blengthindrawinglengthinreality+
  • Clengthinrealitylengthindrawing
  • Dlengthindrawinglengthinreality×

This lesson includes 65 additional questions and 486 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.