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×


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?

  • A1=953inchfeet
  • B1=1723inchfeet
  • C1=7023inchfeet
  • D1=2253inchfeet
  • E1=589inchfeet


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.


A map is scaled such that every 18 in is equivalent to 50 mi. How many miles are represented by 4 inches on the map?


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.


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.


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


Given that the distance between two cities on a map is 4.4 cm and the actual distance between them is 26.4 km, what is the drawing scale of the map?

  • A160,000
  • B14,000
  • C124,000
  • D1600,000
  • E1105,600


Complete the table.

Drawing DistanceReal DistanceScaleMagnification or Reduction
4.2 dm30 km
  • A750,000:, reduction
  • B50,0007:, magnification
  • C7500,000:, reduction
  • D500,0007:, magnification


Complete the table.

Drawing Distance Real Distance Scale Magnification or Reduction
cm90 km7900,000
  • A70, reduction
  • B7, reduction
  • C7, magnification
  • D70, magnification


The figure below shows a drawing of the floor plan of a house. The drawing scale is 1100. 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


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 DistanceThe Real DistanceThe ScaleMagnification or Reduction
66 cm mm221
  • A1, magnification
  • B3, magnification
  • C1, reduction
  • D30, magnification
  • E30, reduction


A map is drawn with a drawing scale of 13,800,000. If the actual distance between two cities is 76 km, determine the distance between them on the map.


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?

  • A201:
  • B4061:
  • C21:
  • D2061:


Every inch in a scale model of a car represents 12 ft in reality. If a vehicle is 412 ft long, how long is the scale model?

  • A12 in
  • B214 in
  • C9 in
  • D412 in


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

  • A2
  • B12
  • C13
  • D3
  • E23

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