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What is the area of a trapezoid ABCD as above figure?

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What is the area of a trapezoid ABCD as above figure?  [#permalink]

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New post 10 Aug 2017, 01:16
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

97% (01:08) correct 3% (00:35) wrong based on 45 sessions

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Attachment:
8.10.png
8.10.png [ 4.39 KiB | Viewed 673 times ]


What is the area of a trapezoid ABCD as above figure?

A. 84
B. 96
C. 104
D. 120
E. 150

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Re: What is the area of a trapezoid ABCD as above figure?  [#permalink]

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New post 10 Aug 2017, 01:33
MathRevolution wrote:
Attachment:
8.10.png


What is the area of a trapezoid ABCD as above figure?

A. 84
B. 96
C. 104
D. 120
E. 150


Consider perpendicular from a point E to B.
EC = DC-DE = 16-10=6

Using Pythagorean's Theorem:
BE^2 = BC^2-EC^2 = 100-36 = 64
BE = 8

Area of trapezoid= BE*(AB+CD)*1/2 = 8*13 = 104.

C.
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What is the area of a trapezoid ABCD as above figure?  [#permalink]

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New post 10 Aug 2017, 03:41
A right angled triangle formed if the rectangle is completed(which is otherwise missing from the picture)

The right angled triangle has hypotenuse - 10 and height 6(16-10).
Therefore the base can be got by \(\sqrt{10^2 - 6^2} = 8\)

The area of the triangle is \(\frac{1}{2}\)*Base*Height = \(\frac{1}{2}*8*6 = 24\)
The rectangle has area of \(16*8 = 128\)

Area of trapezoid = Area(Rectangle) - Area(Triangle) \(= 128 - 24 = 104\)(Option C)
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Re: What is the area of a trapezoid ABCD as above figure?  [#permalink]

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New post 13 Aug 2017, 18:20
==> The area of a trapezoid is (base1+base2)height/2.
Attachment:
AA.png
AA.png [ 4.11 KiB | Viewed 547 times ]

As shown above, the height becomes 8. Then, the area becomes (16+10)8/2=26*4=104.

The answer is C.
Answer: C
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Re: What is the area of a trapezoid ABCD as above figure?   [#permalink] 13 Aug 2017, 18:20
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What is the area of a trapezoid ABCD as above figure?

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