Lesson 11-7 Ratios of Areas (page 456)

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Presentation transcript:

Lesson 11-7 Ratios of Areas (page 456) Essential Question How can you calculate the area of any figure?

Comparing Areas of Triangles (1) If two triangles have equal heights, then the ratio of their areas equals the ratio of their bases .

Comparing Areas of Triangles (2) If two triangles have equal bases, then the ratio of their areas equals the ratio of their heights .

Comparing Areas of Triangles (3) If two triangles are similar, then the ratio of their areas equals the square of their scale factor . WHY?

Here is why. ~ ∆’s by AA~ , then S.F. 4 Asmall ∆ 3 Alarge ∆ 8 9

Theorem 11-7 If the scale factor of two similar figures is a: b , then: (1) the ratio of the perimeters is a : b. (2) the ratio of the areas is a2 : b2.

#1 The scale factor of two similar figures is 3 : 5 #1 The scale factor of two similar figures is 3 : 5. Find the ratio of the perimeters and the ratio of the areas. ratio of perimeters = _______ ratio of areas = _________ 3 : 5 9 : 25

#2 The ratio of the areas of two similar figures is 1 : 4 #2 The ratio of the areas of two similar figures is 1 : 4 . Find the ratio of their perimeters. ratio of perimeters = _______ 1 : 2 1 : 4

#3 The areas of two circles are 36π and 64π #3 The areas of two circles are 36π and 64π. Find the ratios of the diameters and circumferences. ratio of diameters = _______ ratio of circumferences = _______ 3 : 4 3 : 4

#4 The scale factor of two quadrilaterals is 3:5 #4 The scale factor of two quadrilaterals is 3:5. The area of the smaller quadrilateral is 27 in2. Find the area of the larger quadrilateral.

How can you calculate the area of any figure? Assignment Written Exercises on pages 458 & 459 REQUIRED: 1 to 15 odd numbers Chapter 11: Areas of Plane Figures project is due _________! How can you calculate the area of any figure?