Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 8 Geometry.

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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 8 Geometry

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 8.4 Area

Martin-Gay, Basic Mathematics, 4e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Areas of Geometric Figures Area Formulas of Common Geometric Figures Rectangle width length Area = length · width A = lw Square side Area = side · side A = s ·s = s 2

Martin-Gay, Basic Mathematics, 4e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Areas of Geometric Figures Area Formulas of Common Geometric Figures Triangle Parallelogram Area = base · height A = b · h

Martin-Gay, Basic Mathematics, 4e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Areas of Geometric Figures Area Formulas of Common Geometric Figures Trapezoid

Martin-Gay, Basic Mathematics, 4e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the area of a triangle. The area is 15 square yards. 6 yds 5 yds

Martin-Gay, Basic Mathematics, 4e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the area. The area is square feet.

Martin-Gay, Basic Mathematics, 4e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the area. The area is 28 square meters. 5 m 9 m 4 m

Martin-Gay, Basic Mathematics, 4e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Circles Area Formula of a Circle radius

Martin-Gay, Basic Mathematics, 4e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the area of the circle. The area is about square centimeters. 2 cm

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 8.5 Volume

Martin-Gay, Basic Mathematics, 4e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Volumes of Solids Volume Formulas of Common Solids

Martin-Gay, Basic Mathematics, 4e 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the volume. The volume is 128 cubic cm. 4 cm 8 cm

Martin-Gay, Basic Mathematics, 4e 14 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Volumes of Solids Volume Formulas of Common Solids

Martin-Gay, Basic Mathematics, 4e 15 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Volumes of Solids Volume Formulas of Common Solids

Martin-Gay, Basic Mathematics, 4e 16 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Approximate the volume of the ball with a 3 inch radius. Use the approximation Give an exact answer and an approximate answer. Exact Approximate

Martin-Gay, Basic Mathematics, 4e 17 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Volumes of Solids Volume Formulas of Common Solids

Martin-Gay, Basic Mathematics, 4e 18 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Approximate the volume of the can. Use Give an exact volume and an approximate volume. Exact continued 1 1

Martin-Gay, Basic Mathematics, 4e 19 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued Approximate the volume of the can. Use Give an exact volume and an approximate volume. Approximate 11 11

Martin-Gay, Basic Mathematics, 4e 20 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Volumes of Solids Volume Formulas of Common Solids

Martin-Gay, Basic Mathematics, 4e 21 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Approximate the volume of the cone. Use Give an exact answer and an approximate answer. Approximate continued

Martin-Gay, Basic Mathematics, 4e 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued Approximate the volume of the cone. Use Give an exact answer and an approximate answer. Exact The volume is approximately cubic centimeters.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 8.6 Square Roots and The Pythagorean Theorem

Martin-Gay, Basic Mathematics, 4e 24 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding Square Roots Square Root of a Number A square root of a number a is a number b whose square is a. We use the radical sign to name square roots. In symbols,

Martin-Gay, Basic Mathematics, 4e 25 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find each square root. a. b. c.

Martin-Gay, Basic Mathematics, 4e 26 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Approximate each square root to the nearest thousandth. a. b. c.

Martin-Gay, Basic Mathematics, 4e 27 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Using the Pythagorean Theorem Pythagorean Theorem In any right triangle, (leg) 2 + (other leg) 2 = (hypotenuse) 2 hypotenuse leg

Martin-Gay, Basic Mathematics, 4e 28 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Using the Pythagorean Theorem Finding an Unknown Length of a Right Triangle

Martin-Gay, Basic Mathematics, 4e 29 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the length of the hypotenuse of the given right triangle. 48 m 22 m The hypotenuse is approximately 53 meters long.

Martin-Gay, Basic Mathematics, 4e 30 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the length of the leg of the given right triangle. 3 yd 9 yd The leg is approximately 8 yards long.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 8.7 Congruent and Similar Triangles

Martin-Gay, Basic Mathematics, 4e 32 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Congruent Triangles Two triangles are congruent when they have the same shape and same size.

Martin-Gay, Basic Mathematics, 4e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Congruent Triangles

Martin-Gay, Basic Mathematics, 4e 34 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Congruent Triangles

Martin-Gay, Basic Mathematics, 4e 35 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the length of the side labeled n of the following pair of similar triangles. 8 9 n 14 Since the triangles are similar, corresponding sides are in proportion. Thus, the ratio of 8 to 14 is the same as the ratio of 9 to n. continued

Martin-Gay, Basic Mathematics, 4e 36 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example The missing length is units.

Martin-Gay, Basic Mathematics, 4e 37 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Mel Rose is a 6-foot tall park ranger who needs to know the height of a particular tree. He measures the shadow of the tree to be 69 feet long when his own shadow is *9 feet long. Find the height of the tree. continued

Martin-Gay, Basic Mathematics, 4e 38 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Continued The height of the tree is 46 feet.