**Problem 2: Consider the trapezoid below.**- **Diagram:** - The diagram displays a trapezoid with height \( h \), and two bases with lengths \( a \) and \( b \).**Instructions:****(a)** Decompose this trapezoid into shapes that we know how to find the area of, i.e., triangles, rectangles, or parallelograms.**(b)** Use the decomposition you found above to express the area of the trapezoid in terms of \( a \), \( b \), and \( h \).**(c)** Make two copies of this parallelogram and put those two copies together in a way that creates a shape we know how to find the area of.**(d)** Use the shape you created above to express the area of the trapezoid in terms of \( a \), \( b \), and \( h \).**(e)** Are the formulas you found in part 2b and part 2d equivalent?**Graph/Diagram Explanation:**- The trapezoid is labeled with its bases \( a \) and \( b \), and height \( h \). You need to visualize decomposing and rearranging this trapezoid in multiple ways to calculate its area, helping reinforce the understanding of geometric properties and area calculations.

Given trapezoid:Decomposition of this trapezoid into shapes that we know how to find the area is shown as: First shape is parallelogram with base length a and the height of h. Second shape is a triangle with the base length of (b-a) and the height of h.The area of trapezoid using the above decomposition is given as: Area of trapezoid=Area of parallelogram+Area of triangleA=base×height+12×base×heightA=a×h+12b-ahA=ah+12bh-ahA=ah+bh2-ah2A=ah2+bh2A=ah+bh2A=a+bh2 Therefore, The area of the trapezoid in terms of a, b, and h is 12a+bh Two copies of this parallelogram is shown as: On putting those two copies together in a way that creates a shape we know how to find the area of is shown as: The shape is a parallelogram with the base length of 2a.

Answered: (a) Decompose this trapezoid into…

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Algebra

(a) Decompose this trapezoid into shapes that we know how to find the area of, i.e. triangles, rectangles, or parallelograms.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Problem 2: Consider the trapezoid below.**

- **Diagram:**
- The diagram displays a trapezoid with height \( h \), and two bases with lengths \( a \) and \( b \).

**Instructions:**

**(a)** Decompose this trapezoid into shapes that we know how to find the area of, i.e., triangles, rectangles, or parallelograms.

**(b)** Use the decomposition you found above to express the area of the trapezoid in terms of \( a \), \( b \), and \( h \).

**(c)** Make two copies of this parallelogram and put those two copies together in a way that creates a shape we know how to find the area of.

**(d)** Use the shape you created above to express the area of the trapezoid in terms of \( a \), \( b \), and \( h \).

**(e)** Are the formulas you found in part 2b and part 2d equivalent?

**Graph/Diagram Explanation:**
- The trapezoid is labeled with its bases \( a \) and \( b \), and height \( h \). You need to visualize decomposing and rearranging this trapezoid in multiple ways to calculate its area, helping reinforce the understanding of geometric properties and area calculations.

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