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# Geometry

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Suppose that ABCD is a trapezoid in which AD || BC. Given AC perpendicular CD,  AC bisects angle BAD, and the area of ABCD is 42, then compute the area of triangle ACD.

Dec 16, 2018
edited by EmperioDaZe  Dec 16, 2018
edited by EmperioDaZe  Dec 20, 2018

#1
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What is the length of AD or AC? We need the length of some sides to determine what the area is. Many trapezoids that fit your description could have different side lengths, leading to different areas.

I cannot help you too much because insufficient information was given, but I can tell you that ABCD is an isosceles trapezoid. Angle ADC = Angle BCD, Angle DAB = Angle CBA. Since AC bisects angle DAB, DB also bisects angle ABC.

- PM

Dec 16, 2018
#2
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[ABCD] = 42

EmperioDaZe  Dec 16, 2018
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I am not sure.

PartialMathematician  Dec 16, 2018
edited by PartialMathematician  Dec 17, 2018
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PartialMathematician  Dec 16, 2018
edited by PartialMathematician  Dec 17, 2018
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"The intersection of AC and DB is Point O.

Since the top triangle (ABO) is 4 times smaller than the bottom triangle (DOC), and the triangles on the side are the same area. "

What are you talking about PM ?   This makes no sense.

Melody  Dec 16, 2018
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I think [ABCD] means the area is 42 units^2.

PartialMathematician  Dec 17, 2018
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What does this mean       [ABCD] = 42      ??

I have never seen that notation before.

Dec 16, 2018
#7
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This means the area of ABCD is 42.

CoolStuffYT  Dec 16, 2018
#8
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Why does it mean that? It could mean the preimeter is 42.

I expect you are right but I do not think that is any recognised notation.

If the units as in units squared were given it would be more obvious.

Melody  Dec 16, 2018
#10
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It means area

Dec 20, 2018
#11
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It means area

Dec 20, 2018