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Geometry Notes: Section 11.3 Perimeters & Areas of Similar Figures Name________________________ Goals: Compare _____________ and _______________ of ________________ figures. Use ______________ and _____________ to solve _______________. Investigation: Draw a rectangle that is 3 x 2 … Find its area…________ Draw a rectangle that 6 x 4 … Find its area…________ What lengths of sides were doubled, did the areas doubled?__________ Let’s see what happened… Find the ratio of the sides … _________ Find the ratio of the areas … __________ Theorem: The Area of similar Polygons: If 2 polygons are ______________ with lengths of _________________ sides to be in the ratio of __________, then the ratio of their areas is ______________ . Ex 1) ABCDE ~ MNOPQ C D B E A 4 Find the ratio of the areas.___________________ O P N M 6 Q Ex 2) These figures are similar. The area of the smaller one is 20. Find the area of the larger picture. 4 10 Your turn… ...These 2 figures are similar. The area of the larger figure is 320. Find the area of the smaller figure. 5 8 Try it again… …These 2 figures are similar. The area of the larger figure is 720. Find the area of the smaller figure. 12 5 Problem… …If the figures are similar, what is the length of the side labeled x? Remember: A = 36 4 The ratio of the areas is the square of the ratios of the sides OR The ratio of the sides is the square A = 100 x root of the ratio of the areas! Here’s nothing surprising… If 2 polygons are similar, the ratio of the perimeters is equal to the ratio of sides. 3 6 2 4 Perimeter=______ Perimeter=______ Ex) ABCD ~ DEFG AB = _______ and DE = _______ The perimeter of ABCD is 20. What is the perimeter of DEFG?_______ SUMMARY: The ratio of the ______________ of similar figures is the ____________ of the ratio of the sides. The ratio of the ______________ of similar figures is the ________ as the ratio of the sides. The ratio of the _____________ in two similar figures is the __________ _______ of the ratio of the areas. Practice Time: 1. RATS ~ DOGS, RA = 12 and DO = 30. a. What is the ratio of the perimeters of RATS to DOGS? ______________ b. What is the ratio of the areas of RATS to DOGS? ______________ 2. Two figures are similar, ABCDE and XYZWS. The perimeter of ABCDE is 3 3 and the perimeter of XYZWS is 18. What is the ratio of the corresponding sides (the scale factor)?_______________ 3. JKL ~ RST. The area of JKL is 25 and the area of RST is 64. What is the ratio of the perimeters?_________ 4. HOT ~ DOG. The area of HOT is 100 and the area of DOG is 9. The perimeter of HOT is 40. What is the perimeter of DOG? ____________________ Practice Time: 1. RATS ~ DOGS, RA = 12 and DO = 30. a. What is the ratio of the perimeters of RATS to DOGS? ______________ b. What is the ratio of the areas of RATS to DOGS? ______________ 2. Two figures are similar, ABCDE and XYZWS. The perimeter of ABCDE is 3 3 and the perimeter of XYZWS is 18. What is the ratio of the corresponding sides (the scale factor)?_______________ 3. JKL ~ RST. The area of JKL is 25 and the area of RST is 64. What is the ratio of the perimeters?_________ 4. HOT ~ DOG. The area of HOT is 100 and the area of DOG is 9. The perimeter of HOT is 40. What is the perimeter of DOG? ____________________ 5. You want to carpet a room that measures 40 ft by 48 ft. An advertisement states tahtt the cost to carpet a room that measures 10 ft by 12 ft is $126. What is a reasonable cost for the larger room? Solution: The ratio of the lengths of corresponding sides are ______________. What is the ratio of the side lengths?__________The ratio of the areas?___________ The carpet for the larger room should cost about ____________ times that of the smaller room. _____________ x ________________ = _________________ A reasonable cost for the larger room is $_____________ 6. A park has two gazebos. The floor of each gazebo has the shape of a regular hexagon. The floor of one gazebo has a perimeter of 72 ft and an area of about 374.12 square feet. The floor of the larger gazebo has a perimeter of 96 feet. Find its area. Solution: All regular hexagons are __________________ because all corresponding angles are _______________ and the corresponding side lengths are _____________________. a) Find the ratio of the perimeters of the two gazebos:_________________ b) Calculate the area of the larger gazebo: (Let A represent the area of the larger gazebo.) The ratio of the area of the smaller gazebo to area larger is: _______ : _______ or _______ : _______ Therefore, the area of the larger gazebo is about _________________ square feet. 5. You want to carpet a room that measures 40 ft by 48 ft. An advertisement states tahtt the cost to carpet a room that measures 10 ft by 12 ft is $126. What is a reasonable cost for the larger room? Solution: The ratio of the lengths of corresponding sides are ____________________________. What is the ratio of the side lengths?____________ The ratio of the areas?_____________ The carpet for the larger room should cost about ____________ times that of the smaller room. _____________ x ________________ = _________________ A reasonable cost for the larger room is $_____________ 6. A park has two gazebos. The floor of each gazebo has the shape of a regular hexagon. The floor of one gazebo has a perimeter of 72 ft and an area of about 374.12 square feet. The floor of the larger gazebo has a perimeter of 96 feet. Find its area. Solution: All regular hexagons are __________________ because all corresponding angles are _______________ and the corresponding side lengths are _____________________. a) Find the ratio of the perimeters of the two gazebos:_________________ b) Calculate the area of the larger gazebo: (Let A represent the area of the larger gazebo.) The ratio of the area of the smaller gazebo to area larger is: _______ : _______ or _______ : _______ Therefore, the area of the larger gazebo is about _________________ square feet.