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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the area of a trapezoid ABCD as above figure? [#permalink]

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10 Aug 2017, 00:16
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Difficulty:

5% (low)

Question Stats:

91% (00:48) correct 9% (00:52) wrong based on 43 sessions

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Attachment:

8.10.png [ 4.39 KiB | Viewed 454 times ]

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

A. 84
B. 96
C. 104
D. 120
E. 150
[Reveal] Spoiler: OA

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

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10 Aug 2017, 00:33
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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10 Aug 2017, 02:41
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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13 Aug 2017, 17:20
==> The area of a trapezoid is (base1+base2)height/2.
Attachment:

AA.png [ 4.11 KiB | Viewed 328 times ]

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

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Re: What is the area of a trapezoid ABCD as above figure?   [#permalink] 13 Aug 2017, 17:20
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