Scale Factor Word Problems

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. It is used to determine the proportional relationship between the dimensions of a drawing or model and the actual object.

Front

How do you calculate the area of a shape when the side lengths are multiplied by a scale factor?

Back

To find the new area when the side lengths are multiplied by a scale factor, square the scale factor and then multiply it by the original area.

Front

If a drawing has a scale of 1 inch = 7 yards, how would you convert a measurement from inches to yards?

Back

To convert from inches to yards, multiply the number of inches by the scale factor (7 yards per inch).

Front

What is the formula for finding the area of a rectangle?

Back

The area of a rectangle is calculated using the formula: Area = length × width.

Front

If a rectangle has a length of 10 cm and a width of 5 cm, what is its area?

Back

The area is 10 cm × 5 cm = 50 cm².

Front

What happens to the area of a rectangle if each side length is doubled?

Back

If each side length is doubled, the area increases by a factor of 4 (since 2² = 4).

Front

How do you find the actual distance between two points on a map given the scale?

Back

To find the actual distance, multiply the distance on the map by the scale factor.

Front

If a map scale is 1 cm = 8 km, what is the actual distance for 5 cm on the map?

Back

The actual distance is 5 cm × 8 km/cm = 40 km.

Front

What is the relationship between scale drawings and real-life dimensions?

Back

Scale drawings represent real-life dimensions in a proportional manner, allowing for accurate representation of size and distance.

Front

How do you determine the scale of a drawing if you know the dimensions of the drawing and the actual object?

Back

To determine the scale, divide the actual dimension by the dimension in the drawing.