Scale Factor Basics
Two similar triangles have side lengths of 6 cm and 12 cm. What is the scale factor from the smaller to the larger triangle?
2
A rectangle has length 8 cm and width 5 cm. What is its area?
40 cm²
On a map, 1 inch = 5 miles. If two cities are 3 inches apart on the map, how far apart are they in real life?
15 miles
A blueprint shows a classroom that is 2 in by 3 in. The scale is 1 in = 5 ft. What are the real dimensions?
10 ft by 15 ft
The scale factor between two similar rectangles is 4. If the smaller has area 10 cm², what is the larger’s area?
160 cm²
A rectangle is reduced by a factor of 0.5. What happens to its area?
It becomes 1/4 the original area.
Both dimensions of a rectangle are doubled. How many times greater is the new area compared to the old one?
4 times greater
A model airplane is built with a scale of 1 cm = 4 m. If the wing measures 5 cm on the model, what is the actual length?
20 m
A cafeteria is 15 cm by 9 cm on a model. If 1 cm = 5 ft, what are the actual dimensions?
75 ft by 45 ft
A triangle’s sides are multiplied by 2. What happens to its perimeter and area?
Perimeter doubles, area quadruples
If a square has side length 3 cm and is enlarged with a scale factor of 4, what is the new side length?
12 cm
A triangle has base 10 cm and height 12 cm. If both are scaled by a factor of 3, what is the new area?
540 cm²
Janet’s room measures 16 ft by 13 ft. On her scale drawing, the room is 4 in by 3.25 in. What is the scale?
1 in = 4 ft
A rug is 3 m by 4 m. A similar rug is enlarged by a factor of 2. What is the new area?
48 m²
If the area of a triangle is 24 cm², and both dimensions are increased by a scale factor of 5, what is the new area?
600 cm²
The perimeter of a triangle is 15 cm. If all sides are doubled, what is the new perimeter?
30 cm
A trapezoid’s area is 50 cm². If scaled by a factor of 2, what is its new area?
200 cm²
Sam builds a model of a 120 m tall building. His model is 60 cm tall. What is the scale?
1 cm = 2 m
A rectangle is scaled with a factor of 3. If the original area is 20 cm², what is the new area?
180 cm²
A cabin floorplan has a scale of 1 cm = 2 m. The drawing shows 14 cm by 16 cm. What is the actual area?
896 m²
If a rectangle’s length and width are both tripled, by what factor does the area increase?
9
A figure’s side lengths are multiplied by 5. The perimeter increases by factor 5. By what factor does the area increase?
25
A map has a scale of 1 cm = 50 km. The distance between two towns is 6 cm on the map. What is the real distance?
300 km
A map shows South Dakota as a rectangle 420 km by 189 km. What is the approximate area?
79,380 km²
A building model is 30 cm tall, representing a 90 m building. What is the scale factor?
1 cm = 3 m