Scale and similar shapes
Solve problems involving similar shapes where the scale factor is known or can be found
What a learner can do afterwards
- Find the missing side of a similar rectangle given a scale factor of 3
- Determine the scale factor between two similar triangles from given side lengths
- Use a scale factor to enlarge or reduce a shape and verify that all sides are in the same ratio
The lesson
Two shapes are similar when they have the exact same shape but different sizes. Every side on the small shape matches a side on the big shape, and all the matching sides are stretched by the same amount. That amount is called the scale factor.
A small rectangle is 4 cm by 6 cm. It is enlarged with a scale factor of 3. Multiply each side by 3: 4 x 3 = 12 cm and 6 x 3 = 18 cm. The new rectangle is 12 cm by 18 cm, and both sides grew by the same scale factor.
To find a missing side, multiply the small shape's side by the scale factor. To find the scale factor itself, divide a big shape's side by the matching small shape's side.
This works for any similar shapes, including triangles, squares, and other polygons. Just make sure you compare matching sides, the ones in the same position on each shape.
Similar shapes have matching sides in the same ratio, so multiply by the scale factor to enlarge and divide to find it.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.