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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
Posts: 7226
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the area of a trapezoid ABCD as above figure?  [#permalink]

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10 Aug 2017, 01:16
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Difficulty:

5% (low)

Question Stats:

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

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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Current Student Status: Preparing for GMAT!! Joined: 11 Oct 2015 Posts: 129 Location: India Concentration: Entrepreneurship, International Business GMAT 1: 660 Q47 V34 GMAT 2: 700 Q48 V38 GPA: 3.1 WE: General Management (Entertainment and Sports) Re: What is the area of a trapezoid ABCD as above figure? [#permalink] Show Tags 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. _________________ Yours, Siva Rama Krishna Meka Senior PS Moderator Joined: 26 Feb 2016 Posts: 3386 Location: India GPA: 3.12 What is the area of a trapezoid ABCD as above figure? [#permalink] Show Tags 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) _________________ You've got what it takes, but it will take everything you've got Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7226 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the area of a trapezoid ABCD as above figure? [#permalink] Show Tags 13 Aug 2017, 18:20 ==> The area of a trapezoid is (base1+base2)height/2. Attachment: 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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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