Find the Scale Factor From Area

Teach shaded area first with Shaded Area Between Rectangles, then add circles and triangles. Move to Scale Changes and Perimeter before Scale Changes and Area so students see k and k² side by side.

Find the area ratio and scale factor for 10 figure pairs, such as 12 cm² to 108 cm², then the new perimeter. The directions on the page read: Each row gives the area of a figure and of a scaled copy. Write the area ratio, new ÷ original, in simplest form. The scale factor k is its square root. Then find the new perimeter, k × P. The page opens with a worked example, and an answer key is included.

Yes, both. We made it for 8th grade geometry, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Find the area of the whole figure, then subtract the area of the white part. A 9 by 6 m rectangle with a 4 by 2.5 m white part has a shaded area of 54 minus 10, or 44 m². Shaded Area Between Rectangles has 6 figures like this.

The area is multiplied by 3², or 9, while the perimeter is multiplied by 3. A 3 ft by 5 ft rug enlarged by k = 3 grows from 15 ft² to 135 ft². Scale Change Word Problems opens with this example.

Write the ratio of the new area to the original area in simplest form, then take its square root. Areas of 44 cm² and 99 cm² give a ratio of 9/4, so k = 3/2. Find the Scale Factor From Area has 10 rows to complete.