Pearson eText for Mathematics for Elementary Teachers with Activities -- Instant Access (Pearson+)

5th Edition

ISBN: 9780137442812

Author: Sybilla Beckmann

Publisher: PEARSON+

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Chapter 12.4, Problem 4P

Figure 12.49 shows a trapezoid. This problem will help you find a formula for the area of the trapezoid and explain in several different ways why this formula is valid.

Chapter 12.4, Problem 4P, Figure 12.49 shows a trapezoid. This problem will help you find a formula for the area of the , example 1

Figure 12.49 A trapezoid.

Show how to combine two copies of the trapezoid in Figure 12.49 to make a parallelogram. Then use the formula for the area of a parallelogram to deduce a formula for the area of the trapezoid. Explain your reasoning.
Show how to cut off portions of the top part of the trapezoid and combine these portions with the bottom part of the trapezoid so as to make one or several parallelograms or rectangles, each of which has one side of length §h.Use this method to deduce a formula for the area of the trapezoid. Explain your reasoning.
By subdividing the trapezoid into two triangles, as shown in Figure 12.50 , find a formula in terms of a, b, and h for the area of the trapezoid, and explain why your formula is valid.

Chapter 12.4, Problem 4P, Figure 12.49 shows a trapezoid. This problem will help you find a formula for the area of the , example 2

Figure 12.50 A subdivided trapezoid.

Besides the methods of parts (a), (b), and (c) of this problem, there are still other methods for deducing the formula for the area of a trapezoid by using the moving and additivity principles. Find another method. Explain your reasoning

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Chapter 12.4, Problem 3P

Chapter 12.4, Problem 5P

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Chapter 12 Solutions

Pearson eText for Mathematics for Elementary Teachers with Activities -- Instant Access (Pearson+)

Ch. 12.1 - You have a 5-foot-by-7-foot rectangular rug in...Ch. 12.1 - Draw a 3-cm-by-7-cm rectangle. Then discuss the...Ch. 12.1 - a. Explain how to decompose the large rectangle in...Ch. 12.1 - a. Explain how to decompose the large rectangle in...Ch. 12.1 - Draw a (fairly long) line segment and designate it...Ch. 12.2 - Make a shape that has area 25in2 but that has no...Ch. 12.2 - Flgure 12.14 shows the floor plan for a one-story...Ch. 12.2 - An area problem: The Johnsons are planning to...Ch. 12.2 - Figure 12.15 shows a design for an herb garden,...Ch. 12.2 - Figure 12.16 [g shows the floor plan for a modern,...

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