Name Class 10-4 Date Practice Form G Perimeters and Areas of Similar Figures Th e fi gures in each pair are similar. Compare the fi rst fi gure to the second. Give the ratio of the perimeters and the ratio of the areas. 1. 2. 6 mm 3 in. 6 in. 8 mm 1 i 2; 1 i 4 4 i 3; 16 i 9 3. 4. 10 m 8 ft 15 m 2 i 3; 4 i 9 20 ft 5 i 2; 25 i 4 Th e fi gures in each pair are similar. Th e area of one fi gure is given. Find the area of the other fi gure to the nearest whole number. 5. 4 in. 8 in. 6. 14 ft area of smaller triangle 5 12 in.2 21 ft area of smaller parallelogram 5 72 ft 2 48 in.2 162 ft2 7. 8. 24 cm 6m 8 cm area of larger pentagon 5 135 cm2 15 cm2 15 m area of smaller rhombus 5 60 m 2 375 m2 9. It took James 5 h to paint an 8 ft by 24 ft wall. At this rate, how long would it take him to paint a 12 ft by 36 ft wall? 11.25 h Find the scale factor and the ratio of perimeters for each pair of similar fi gures. 10. two regular pentagons with areas 144 in. 2 and 36 in. 2 11. two rectangles with areas 72 m2 and 50 m2 2 i 1; 2 i 1 6 i 5; 6 i 5 12. two regular pentagons with areas 147 ft 2 and 12 ft 2 7 i 2; 7 i 2 13. two equilateral triangles with areas 121 " 3 cm 2 and 16 " 3 cm 2 11 i 4; 11 i 4 14. two circles with areas 12p in.2 and 27p in.2 2 i 3; 2 i 3 Name Class 10-4 Date Practice (continued) Form G Perimeters and Areas of Similar Figures Th e scale factor of two similar polygons is given. Find the ratio of their perimeters and the ratio of their areas. 15. 5 i 1 18. 16. 2 i 7 2 i 7; 4 i 49 5 i 1; 25 i 1 10 10 ; 100 7 7 49 17. 3 9 ; 4 4 16 5 5 25 20. 9 9 ; 81 19. 10 i 3 10 i 3; 100 i 9 Algebra Find the values of x and y when the smaller similar rectangle shown here has the area given. 3 8 ft x y 21. 10 ft2 2 ft; 5 ft 22. 20 24. 40 ft2 4 ft; 10 ft ft2 2 " 2 ft; 5 " 2 ft 25. 44.1 ft2 4.2 ft; 10.5 ft 23. 22.5 20 ft ft2 3 ft; 7.5 ft 26. 50 ft22 " 5 ft; 5 " 5 ft 27. Th e area of a regular octagon is 45 ft2 . What is the area of a regular octagon with sides 13 the length of sides of the larger octagon? 5 ft2 28. Th e longer base of a right trapezoid is 12 ft. Th e longer base of a similar right trapezoid is 30 ft. The area of the smaller right trapezoid is 20 ft2 . What is the area of the larger right trapezoid? 125 ft2 29. A postcard costs $0.95. Leslie wants to buy a poster that is a similar shape with a scale factor for the poster to the postcard of 5 i 1. How much should she expect to pay for the poster? $23.75 30. Two similar parallelograms have areas 125 m 2 and 80 m 2 . Th e height of the larger parallelogram is 10 m. What are the lengths of the bases of both parallelograms? 12.5 m and 10 m 31. A team is excavating an archeological site. Th e original plan was to excavate a rectangular area 35 ft long by 20 ft wide. Instead, the team decided to excavate a similar rectangle that is 50 ft wide. Find the length and the area of the new rectangle. 87.5 ft; 4375 ft2 Th e pair of figures is similar. Compare the larger figure to the smaller figure. Find the ratio of their perimeters and the ratio of their areas. 32. 33. 4.5 34. x x 2 5 i 2; 25 i 4 8 3 34 3 3 i 1; 9 i 1 2 i 1; 4 i 1

Perimeters and Areas of Similar Figure

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