Areas of Similar Figures
If we multiply each dimension of a figure by k, then: 1. The new figure is similar to the original figure, and 2. The area of the new figure is k^2 times the area of the original figure. When you scale a 2D shape, you're scaling it in two directions, like length and width. The scaling factor, k, gets applied twice. This means the new area is k \times k or k^2 times the original area. For example: A square with a side length of 5 cm has an area of 25 cm^2. If you scale its dimensions by a factor of k=3, the new.... This skill is part of Grade 8 math in Yoshiwara Core Math.
Key Concepts
Property If we multiply each dimension of a figure by $k$, then: 1. The new figure is similar to the original figure, and 2. The area of the new figure is $k^2$ times the area of the original figure.
Examples A square with a side length of 5 cm has an area of 25 cm$^2$. If you scale its dimensions by a factor of $k=3$, the new side is 15 cm and the new area is $15^2 = 225$ cm$^2$, which is $3^2 \times 25 = 9 \times 25$.
A circular rug has a radius of 2 feet. A larger, similar rug has a radius of 6 feet. The scale factor is 3, so the area of the larger rug is $3^2=9$ times the area of the smaller one.
Common Questions
What is Areas of Similar Figures?
If we multiply each dimension of a figure by k, then: 1. The new figure is similar to the original figure, and 2.
How does Areas of Similar Figures work?
Example: A square with a side length of 5 cm has an area of 25 cm^2. If you scale its dimensions by a factor of k=3, the new side is 15 cm and the new area is 15^2 = 225 cm^2, which is 3^2 \times 25 = 9 \times 25.
Give an example of Areas of Similar Figures.
A circular rug has a radius of 2 feet. A larger, similar rug has a radius of 6 feet. The scale factor is 3, so the area of the larger rug is 3^2=9 times the area of the smaller one.
Why is Areas of Similar Figures important in math?
When you scale a 2D shape, you're scaling it in two directions, like length and width. The scaling factor, k, gets applied twice.
What grade level covers Areas of Similar Figures?
Areas of Similar Figures is a Grade 8 math topic covered in Yoshiwara Core Math in Chapter 6: Core Concepts. Students at this level study the concept as part of their grade-level standards and are expected to explain, analyze, and apply what they have learned.
What are the key rules for Areas of Similar Figures?
The new figure is similar to the original figure, and 2. The area of the new figure is k^2 times the area of the original figure..
What are typical Areas of Similar Figures problems?
A square with a side length of 5 cm has an area of 25 cm^2. If you scale its dimensions by a factor of k=3, the new side is 15 cm and the new area is 15^2 = 225 cm^2, which is 3^2 \times 25 = 9 \times 25.; A circular rug has a radius of 2 feet. A larger, similar rug has a radius of 6 feet. The scale factor is 3, so the area of the larger rug is 3^2=9 times the area of the smaller one.; A triangular garden with an area of 50 square feet is enlarge