Explanation Area of triangle formula: A = 1 2 b h b is the base of the triangle. h is the height of the triangle. Area of trapezoid formula: A = 1 2 ( a + b ) h a is the short base of the triangle. b is the long base of the triangle. h is the height of the triangle. Pythagorean Theorem: For any right triangle with sides of length a and b and hypotenuse length c , a 2 + b 2 = c 2 Calculation: Given: There are two ways to complete the proof of James Garfield. We have to use area formula of a trapezoid. We have to add the areas of the three right triangles to find the area of trapezoid. Now we have to find the area of the trapezoid. From the given diagram, we find that h = a + b , a = a , b = b A = 1 2 ( a + b ) ( a + b ) = 1 2 ( a ( a + b ) + b ( a + b ) ) = 1 2 ( a 2 + a b + a b + b 2 ) = 1 2 ( a 2 + 2 a b + b 2 ) Now we have to find the areas of three right triangles and add those areas. To find the area of Δ A O D A = 1 2 b a To find the area of Δ C O D

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

12th Edition

ISBN: 9780321987297

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott

Publisher: PEARSON

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Chapter 14.3A, Problem 16A

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The proof of James Garfield.

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Chapter 14.3A, Problem 15A

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Chapter 14 Solutions

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

Ch. 14.1 - In track, the second lane from the inside of the...Ch. 14.1 - Prob. 3MC Ch. 14.1 - Observe that it is possible to build a triangle...Ch. 14.1 - a. Help each person in the group find his or her...Ch. 14.1 - Jerry wants to design a gold chain 60 cm long made...Ch. 14.1 - A student claims that the circumference of a...Ch. 14.1 - A student asks why 227 cannot always be used as...Ch. 14.1 - A Student imagines a wire stretched around Earth....Ch. 14.1 - Which of these units would be the best to use to...Ch. 14.1 - If Freds rope is 12 inches long, about how long is...

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The proof of James Garfield.

Solution Summary: The author explains that there are two ways to complete the proof of James Garfield: using area formula of a trapezoid and adding the areas of three right triangles.

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Chapter 14 Solutions

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The proof of James Garfield.