The two triangles are similar. Find the length marked x.15
The polygons are similar. Find x.24
These triangles are similar. Solve for x.14
Scale up similar solids
Two similar solids have a scale factor of 2:3. The volume of the smaller is 832. Find the volume of the larger.2808
The surface area of a rectangular prism is 36. A similar rectangular prism has a width of 4 where the first has 3. What is its surface area?64
Two similar solids have surface areas 128and 162. The volume of the smaller is 3072. Find the volume of the larger.4374
Corresponding lengths of two similar solids are in the ratio 6:7. If the smaller solid has surface area 360, what is the surface area of the larger?490
Scale down similar solids
The two boxes are similar. The surface area of the larger box is 2662. Find the surface area of the smaller box.1408
A model and a real tank are similar, with lengths in the ratio 6:7. The real one has volume 4116. Find the volume of the model.2592
Two similar square pyramids have base edges 1and 3. The volume of the larger is 162. Find the volume of the smaller.6
A rectangular prism with a width of 9 has surface area 1863. Find the surface area of a similar rectangular prism whose width is 7.1127
Test similarity and give the scale factor
Triangle A has sides 5, 6, 8. Triangle B has sides 40, 30, 25. Are they similar? If so, give the scale factor from A to B.Yes, scale factor 5
One rectangle measures 9 by 3 and another measures 2 by 6. Are the rectangles similar? If so, give the scale factor from the first to the second.Yes, scale factor 32
A photo is 9 by 8, and a print made from it is 24 by 28. Is the print similar to the photo? If so, give the scale factor from the photo to the print.No; 3=928
One triangle has sides 6, 7, 9 and another has sides 18, 27, 23. Are the triangles similar? If so, give the scale factor from the first to the second.No; 3=723
Find perimeters and areas of similar polygons
Two similar rectangles have scale factor 2 : 5. The smaller has perimeter 22. Find the perimeter of the larger.55
Two similar pentagons have scale factor 5 : 6. The smaller has perimeter 10. Find the perimeter of the larger.12
Two similar rectangles have perimeters 32 and 56. The smaller has area 16. Find the area of the larger.49
Two similar triangles have scale factor 3 : 5. The smaller has perimeter 12. Find the perimeter of the larger.20
Two similar solids have sides in the ratio 2:3. The volume of the smaller is 40. Find the larger
Volumes scale by the cube of the ratio.
8 to 27, so multiply by 27 over 8.
The answer is 135.
Where students go wrong
Scaling area or volume by the plain ratio. Doubling every length multiplies area by four and volume by eight, not two, which is why a scale model weighs so much less than it looks like it should.
Also called similar figures, ratio of areas or ratio of volumes.
What you can put on this worksheet
Matching sides, from the diagram
These triangles are similar. Solve for x.— two similar triangles, labeled x, 5, 8, 10→ 4
Matching sides, from a description
A side of one polygon measures 6 and the matching side of a similar larger polygon measures 18. Another side of the first is 7. Find its match.→ 21
From the smaller solid to the larger
Two similar triangular prisms have heights 3and 4. The volume of the smaller is 54. Find the volume of the larger.→ 128
From the larger solid to the smaller
A cone with a height of 4 has surface area 80. Find the surface area of a similar cone whose height is 3.→ 45
Are they similar? The scale factor
A photo is 2 by 5, and a print made from it is 20 by 8. Is the print similar to the photo? If so, give the scale factor from the photo to the print.→ Yes, scale factor 4
Perimeters and areas of similar polygons
Two similar hexagons have scale factor 2 : 5. The smaller has perimeter 16. Find the perimeter of the larger.→ 40
Questions about these worksheets
Yes. Every similar figures sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the similar figures questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 6: matching sides, from the diagram, matching sides, from a description, from the smaller solid to the larger, from the larger solid to the smaller, are they similar? the scale factor and perimeters and areas of similar polygons. Tick as many as you want and set how many of each, or let it spread them evenly.
Scaling area or volume by the plain ratio. Doubling every length multiplies area by four and volume by eight, not two, which is why a scale model weighs so much less than it looks like it should.