Geometry/TrigName: __________________________ Ratio of Perimeters & Areas ExplorationDate: ___________________________ Recall – Similar Figures are figures that have congruent corresponding angles and proportional corresponding sides. You can calculate the scale factor for a set of similar figures. Example – Calculate the scale factor from  ABC to  GHI. A BC H G I Scale Factor of  ABC to  GHI: __________ Now, calculate the Perimeter and Area of each triangle. Perimeter of  ABC: _____________Perimeter of  GHI: ______________ Area of  ABC: _________________Area of  GHI: __________________ From  ABC to  GHI… What is the ratio of side lengths? _______________________ What is the ratio of perimeters? ________________________ What is the ratio of areas? _____________________________ What do you notice? ______________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ Rule: Scale Factor of Similar Figures: _____________________________________________ Ratio of Perimeters of Similar Figures: ________________________________________ Ratio of Areas of Similar Figures: ____________________________________________ A pair of ________________ or_________________ are always similar to one another.

Directions – Find the Area and Perimeter of each set of similar figures. Examine the ratios of Perimeters to Areas and make sure that they follow the rule from your exploration. 1. Rectangles2. Triangles 4. The perimeter of two similar polygons is 24 to 28. Find each of the following: Ratio of Perimeters: _________________ Ratio of Side Lengths: ________________ Ratio of Areas: _____________________ 3. The areas of two circles are 36  and 64 . Find each of the following: Ratio of Areas: _____________________ Scale Factor: _______________________ Ratio of Circumferences: ______________ Radius of Smaller Circle: ______________ Radius of Larger Circle: _______________ Circumference of Smaller Circle: ________ Circumference of Larger Circle: _________ Perimeters: ___________ and __________ Areas: ___________ and _____________ Scale Factor: _______________________ Ratio of Perimeters: __________________ Ratio of Areas: ______________________ Perimeters: ___________ and __________ Areas: ___________ and _____________ Scale Factor: _______________________ Ratio of Perimeters: __________________ Ratio of Areas: ______________________ 5. The scale factor of two similar figures is 2:3. The area of the larger figure is 27. Find the area of the smaller figure. 5. The scale factor of two similar polygons is 3:4. One side of the larger polygon is 20. Find the length of the corresponding side length in the smaller polygon. 6. The areas of two similar polygons are 50 and 72. The perimeter of the smaller polygon is 30. Find the perimeter of the larger polygon.