Presentation on theme: "11-5 Areas of Similar Figures You used scale factors and proportions to solve problems involving the perimeters of similar figures. Find areas of similar."— Presentation transcript:
11-5 Areas of Similar Figures You used scale factors and proportions to solve problems involving the perimeters of similar figures. Find areas of similar figures by using scale factors. Find scale factors or missing measures given the areas of similar figures.
Similarity, Perimeter, and Area Rectangle A Rectangle B 1.What is the length and width of each rectangle? 2.What similarity ratio was used? 3.Find the perimeter of each rectangle. 4.Find the area of each rectangle.
Similarity, Perimeter, and Area 1.What is the length of the sides of each square? 2.What similarity ratio was used? 3.Find the perimeter of each square. 4.Find the area of each square.
How do the similarity ratios of the polygon relate to the ratios of their perimeters and areas? Shape Sim ratioP-ratioA-ratio Rectangle 2 / 1 2 / 1 4 / 1 Square 1 / 3 1 / 3 1 / 9 Pattern ( ) 1 ( ) 1 ( ) 2
Areas of Similar Figures If two polygons are similar, their perimeters are proportional to their scale factor. If two polygons are similar, their area are proportional to the square of their scale factor. p. 818
ABCDE ~ GHIJK. The similarity ratio of ABCDE to GHIJK is 2. A B C D E H I J K G 1.If the perimeter of GHIJK is 10 cm, what is the perimeter of ABCDE? 2.If the area of ABCDE is 24 cm 2, what is the area of GHIJK? 20 cm 6 cm 2
If ABCD ~ PQRS and the area of ABCD is 48 square inches, find the area of PQRS. The scale factor between PQRS and ABCD is or. So, the ratio of the areas is __ 9 6 3 2 Write a proportion. Multiply each side by 48. Simplify.
A.180 ft 2 B.270 ft 2 C.360 ft 2 D.420 ft 2 If EFGH ~ LMNO and the area of EFGH is 40 square inches, find the area of LMNO.
The area of ΔABC is 98 square inches. The area of ΔRTS is 50 square inches. If ΔABC ~ ΔRTS, find the scale factor from ΔABC to ΔRTS and the value of x. Let k be the scale factor between ΔABC and ΔRTS. Theorem 11.1 Substitution Take the positive square root of each side. Simplify. So, the scale factor from ΔABC to ΔRTS is Use the scale factor to find the value of x.
The ratio of corresponding lengths of similar polygons is equal to the scale factor between the polygons. Substitution 7x= 14 ● 5Cross Products Property. 7x= 70Multiply. x= 10Divide each side by 7. Answer:x = 10
A.3 inches B.4 inches C.6 inches D.12 inches The area of ΔTUV is 72 square inches. The area of ΔNOP is 32 square inches. If ΔTUV ~ ΔNOP, use the scale factor from ΔTUV to ΔNOP to find the value of x.