Explanation Allowing for degenerate trapezoids we have 0 ≤ θ ≤ π via trigonometry and surgery (slice off a right triangle and rearrange trapezoid into a rectangle) Rectangle of base 4 − 2 cos θ height 2 sin θ A ( θ ) = ( 4 − 2 cos θ ) , 2 sin = 8 sin θ − 4 sin θ cos θ = 8 sin θ − 2 sin 2 θ Where 0 ≤ θ π A ' ( θ ) = 8 cos θ − 4 cos 2 θ = 4 + 8 cos θ − 8 cos 2 θ = 0 For 0 ≤ θ ≤ π to obtain θ = θ 0 = cos − 1 ( 1 − 3 2 ) ≈ 1

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.6, Problem 34E

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Find the angle θ that maximize the area of the trapezoid with a base of length 4 and sides of length 2

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Chapter 4.6, Problem 33E

Chapter 4.6, Problem 35E

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Find the angle θ that maximize the area of the trapezoid with a base of length 4 and sides of length 2

Solution Summary: The author explains that the angle theta maximizes the area of the trapezoid with a base of 4 and sides of 2; it can be solved since A(0)=A(p

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