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Quadrilateral ABCD is a parallelogram,r=2,and DAB=45,what is the area

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Afroditee
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Quadrilateral ABCD is a parallelogram,r=2,and DAB=45,what is the area [#permalink] New post   18 Oct 2022, 07:53
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55% (hard)

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65% (02:44) correct 35% (02:25) wrong based on 23 sessions
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Quadrilateral ABCD is a parallelogram , r=2,and ∠DAB=45,what is the area of the shaded region?

A.\( \sqrt{2}\) - \(\frac{π}{3}\)

B. \(\sqrt{2}\) - \(\frac{π}{2}\)

C. 2\(\sqrt{2}\) - \(\frac{π}{2}\\
\)

D. 2\(\sqrt{ 2}\) - \(\frac{π}{3}\\
\)

E. 2 \(\sqrt{2}\) - \(\frac{π}{4}\)
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C
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Quadrilateral ABCD is a parallelogram,r=2,and DAB=45,what is the area [#permalink] New post   18 Oct 2022, 09:15
Area of sector = Q/360* π r^2= 45/360 * π *4 = π /2
Area of parallelogram (rhombus) = a^2sinQ = 4*sin45 = 2√2

Area of shaded region =2√2 - π /2
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Re: Quadrilateral ABCD is a parallelogram,r=2,and DAB=45,what is the area [#permalink] New post   10 Dec 2022, 12:10
jim441 wrote:
Area of sector = Q/360* π r^2= 45/360 * π *4 = π /2
Area of parallelogram (rhombus) = a^2sinQ = 4*sin45 = 2√2

Area of shaded region =2√2 - π /2

Could you solve it without trigonometry?

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Quadrilateral ABCD is a parallelogram,r=2,and DAB=45,what is the area [#permalink] New post   10 Dec 2022, 13:33
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Area of the shaded region = Area of the parallelogram - Area of the arc ABD

The detailed working is shown.

Option C
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Quadrilateral ABCD is a parallelogram,r=2,and DAB=45,what is the area [#permalink]
10 Dec 2022, 13:33
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