Name: _________________________________________________ Period: ___________ Date: ________________ Perimeters and Areas of Similar Figures Assignment The figures in each pair are similar. Compare the first figure to the second. Find the scale factor and give the ratio of the perimeters and the ratio of the areas. ππ 1. 2. π π πππππ π πππππ πππππ ππ ππππππππππ πππππ ππ πππππ πππππ π πππππ 3. ππ πππππ ππ ππππππππππ πππππ ππ πππππ 4. π. π π. π ππ πππππ π πππππ πππππ ππ ππππππππππ πππππ ππ πππππ π πππππ π πππππ πππππ ππ ππππππππππ πππππ ππ πππππ The figures in each pair are similar. The area of one figure is given. Find the area of the other figure 5. 6. ππ ππ π ππ ππ. π¨π = ππ ππ π¨π =? π¨π =? Copyright © GeometryCoach.com 1 π ππ. π¨π = ππππ.π Name: _________________________________________________ Period: ___________ Date: ________________ Perimeters and Areas of Similar Figures Assignment 7. 8. ππ. π ππ π. πππ ππ ππ π¨π = πππππππ π ππ π¨π =? π¨π =? π¨π = ππππππ Find the scale factor and the ratio of perimeters for each pair of similar figures. 9. 10. π¨π = πππππ Copyright © GeometryCoach.com π¨π = ππππππ π¨π = πβππππ 2 π¨π = πππβππππ Name: _________________________________________________ Period: ___________ Date: ________________ Perimeters and Areas of Similar Figures Assignment Find the value of x! 11. 12. ππ π π. π π π ππ π π ππ ππ. ππ ππ. Find the scale factor and the ratio of perimeters for each pair of similar figures. 13. Two regular hexagons with areas: π¨π = ππ πππ π¨π = ππ πππ 14. Two regular octagons with areas: π¨π = πππ ππ π¨π = ππ ππ 15. Two equilateral triangles with areas: π¨π = πππβπ πππ π¨π = πππβπ πππ Copyright © GeometryCoach.com 3 πππ ππ. Name: _________________________________________________ Period: ___________ Date: ________________ Perimeters and Areas of Similar Figures Assignment Solve each problem! 16. The area of a regular octagon is ππ ππ . What is the π area of a regular octagon with sides π the length of sides of the larger octagon? 17. The similarity ratio of two similar polygons is π: π. The perimeter of the larger polygon is πππ ππ. What is the perimeter of the smaller polygon? 18. The lengths of the sides of two triangles are in the similarity ratio of π: π. If the area of the larger triangle is πππ ππ , find the area of the smallest triangle. 19. The ratio of the perimeters of two similar hexagons is π: π.The area of larger hexagon is πππ ππ.π What is the area of the smaller hexagon? 20. Two similar parallelograms have areas ππ ππ and ππ ππ . The height of the larger parallelogram is ππ π. What are the lengths of the bases of both parallelograms? Copyright © GeometryCoach.com 4 Name: _________________________________________________ Period: ___________ Date: ________________ Perimeters and Areas of Similar Figures Assignment ANSWERS The figures in each pair are similar. Compare the first figure to the second. Find the scale factor and give the ratio of the perimeters and the ratio of the areas. ππ 1. 2. π π π π π = = π ππ π πππππ π πππππ π·π π = π·π© π πππππ ππ ππππππππππ π π π = = π ππ π π¨π ππ π = π= π¨π© π ππ πππππ π πππππ πππππ ππ πππππ 3. ππ π·π π = π·π© π πππππ ππ ππππππππππ π¨π ππ π = = π¨π© ππ π πππππ ππ πππππ 4. π. π π. π ππ π π. π π = = π π. π π πππππ π πππππ π·π π = π·π© π πππππ ππ ππππππππππ π π ππ π = = π π π π¨π ππ π = = π¨π© ππ π πππππ π πππππ πππππ ππ πππππ π·π π = π·π© π πππππ ππ ππππππππππ π¨π ππ ππ = = π¨π© ππ π πππππ ππ πππππ The figures in each pair are similar. The area of one figure is given. Find the area of the other figure 5. 6. ππ ππ π ππ ππ. π¨π = ππ ππ π¨π =? π¨π =? π ππ π = = π ππ π π π¨π ππ π = = π¨π ππ ππ ππππ π = π¨π ππ π¨π = ππ β ππππ π¨π = πππ ππ Copyright © GeometryCoach.com π ππ. π¨π = πππππ π ππ ππ. π = = π π ππ. π π¨π ππ ππ = = π¨π ππ π π¨π ππ = ππ ππ.π π π¨π = ππ ππ.π β ππ π¨π = πππ ππ.π 5 Name: _________________________________________________ Period: ___________ Date: ________________ Perimeters and Areas of Similar Figures Assignment 7. 8. ππ. π ππ π. πππ ππ ππ π¨π = πππππππ π ππ π¨π =? π¨π = ππππππ π¨π =? π ππ π = = π π π π¨π ππ ππ = = π¨π ππ π π¨π ππ = π πππ ππ π π ππ. π ππ π = = π π. π ππ π π π¨π π ππ = π= π¨π π π ππππ πππ ππ = π¨π π πππππππ π¨π = ππ π¨π = ππ β πππ πππ π¨π = ππππ πππ π¨π = ππ πππ Find the scale factor and the ratio of perimeters for each pair of similar figures. 9. 10. π¨π = πππππ π¨π = ππππππ π¨π = πβππππ π¨π ππ πππ π = = π π¨π πππ ππ π π·π βπ¨π βπ π = = = π·π βπ¨π βπ π π π·π π = = π π·π π Copyright © GeometryCoach.com π¨π = πππβππππ π¨π πβπ πππ π = = π π¨π πππβπ ππ πππ π·π βπ¨π π βπ = = = π·π βπ¨π βπππ ππ π π·π π = = π π·π ππ 6 Name: _________________________________________________ Period: ___________ Date: ________________ Perimeters and Areas of Similar Figures Assignment Find the value of x ! 11 . π. π π 12 . ππ π π ππ π π ππ ππ. ππ ππ. π π. π π π = = π ππ π π π π = πππ π π=ππ πππ ππ. π ππ ππ. π = = π πππ ππ. π π π = ππ ππ. π π = π ππ. Find the scale factor and the ratio of perimeters for each pair of similar figures. 13. Two regular hexagons with areas: π¨π = ππ πππ π¨π = ππ πππ π¨π πππππ ππ = = π¨π πππππ ππ π·π βππ π = = π·π βππ π π π·π π = = π π·π π 14. Two regular octagons with areas: π¨π = πππ ππ π¨π = ππ ππ π¨π πππ ππ π = = π¨π ππ ππ π π·π βπ π = = π·π βπ π π π·π π = = π π·π π π¨π πππβπ πππ πππ = = π¨π πππβπ πππ πππ π·π βπππ ππ = = π·π βπππ ππ π π·π ππ = = π π·π ππ 15. Two equilateral triangles with areas: π¨π = πππβπ πππ π¨π = πππβπ πππ Copyright © GeometryCoach.com 7 Name: _________________________________________________ Period: ___________ Date: ________________ Perimeters and Areas of Similar Figures Assignment Solve each problem! 16. The area of a regular octagon is ππ ππ . What is the π area of a regular octagon with sides π the length of sides of the larger octagon? π¨π = ππ ππ π¨π = ? π ππ = ππ π π ππ = π ππ π ππ π = = π π π π π π π¨π ππ ππ π = = = π¨π ππ ππ π ππ ππ π = π¨π π π¨π = π ππ 17. The similarity ratio of two similar polygons is π: π. The perimeter of the larger polygon is πππ ππ. What is the perimeter of the smaller polygon? π π = π π 18. The lengths of the sides of two triangles are in the similarity ratio of π: π. If the area of the larger triangle is πππ ππ , find the area of the smallest triangle. π π = π π 19. The ratio of the perimeters of two similar hexagons is π: π.The area of larger hexagon is πππ ππ.π What is the area of the smaller hexagon? π·π π = π·π π π·π = πππ ππ π·π =? π·π π = π·π π π·π π = πππ ππ π πππ ππ β π π·π = π π·π = ππ ππ π¨π = πππ ππ π¨π π = π¨π π π π¨π ππ = πππ ππ ππ π¨π ππ = π πππ π ππ π¨π = ππ ππ π¨π = πππ ππ.π π π = π π π¨π ππ = π¨π π π π¨π ππ = πππ ππ.π ππ πππ ππ.π β ππ ππ π¨π = πππ ππ.π π¨π = Copyright © GeometryCoach.com 8 π¨π =? π π¨π =? Name: _________________________________________________ Period: ___________ Date: ________________ Perimeters and Areas of Similar Figures Assignment 20. Two similar parallelograms have areas ππ ππ and ππ ππ . The height of the larger parallelogram is ππ π. What are the lengths of the bases of both parallelograms? π¨π = ππ ππ π¨π = ππ ππ ππ =? ππ =? ππ = ππ π π¨π = ππ β ππ ππ ππ = ππ β ππ π ππ = π π π¨π π π π = π¨π π π π ππ ππ = π ππ ππ ππ ππ = π ππ ππ ππ β ππ π ππ = ππ ππ π = ππ ππ = βππ ππ = π π Copyright © GeometryCoach.com 9
© Copyright 2026 Paperzz