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# What is the area of the triangle with points (2,4), (3,6), (5,2)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5585
GMAT 1: 800 Q59 V59
GPA: 3.82
What is the area of the triangle with points (2,4), (3,6), (5,2)? [#permalink]

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27 Sep 2017, 01:41
00:00

Difficulty:

65% (hard)

Question Stats:

63% (01:52) correct 37% (02:25) wrong based on 78 sessions

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[GMAT math practice question]

What is the area of the triangle with points (2,4), (3,6), (5,2)?

A. 4
B. 5
C. 6
D. 7
E. 8

_________________

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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1388 Location: Viet Nam What is the area of the triangle with points (2,4), (3,6), (5,2)? [#permalink] ### Show Tags 27 Sep 2017, 02:06 MathRevolution wrote: [GMAT math practice question] What is the area of the triangle with points (2,4), (3,6), (5,2)? A. 4 B. 5 C. 6 D. 7 E. 8 Draw three points A(2,4), B(3,6) and C(5,2) like this Attachment: Untitled.png [ 10.15 KiB | Viewed 1184 times ] In order to calculate the area of the triangle ABC, we need to calc it in indirect way. Draw point D(5,4). We could easily calculate the area of triangle ACD and ABD. $$S_{ACD}=\frac{1}{2}*3*2=3$$ $$S_{ABD}=\frac{1}{2}*3*2=3$$ So we have $$S_{ABDC}=S_{ACD}+S_{ABD}=3+3=6$$ We could calculate the area of triangle BCD easily. CD=2 and the distance from B to CD is 2. $$S_{BCD}=\frac{1}{2}*2*2=2$$. Now $$S_{ABC}=S_{ABDC}-S_{BCD}=6-2=4$$.. Answer A _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5585 GMAT 1: 800 Q59 V59 GPA: 3.82 What is the area of the triangle with points (2,4), (3,6), (5,2)? [#permalink] ### Show Tags 29 Sep 2017, 01:27 => The area of the triangle with points (a,b), (c,d) and (e,f) is 1| a c e a | 2| b d f b |= (1/2)| ad-bc+cf-de+eb-af | 1| 2 3 5 2 | 2| 4 6 2 4 |= (1/2)| 12-12+6-30+20-4 |= 1/2∙8=4 Ans: A _________________ 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$99 for 3 month Online Course"
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Joined: 06 Aug 2017
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Re: What is the area of the triangle with points (2,4), (3,6), (5,2)? [#permalink]

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30 Sep 2017, 09:18
MathRevolution wrote:
[GMAT math practice question]

What is the area of the triangle with points (2,4), (3,6), (5,2)?

A. 4
B. 5
C. 6
D. 7
E. 8

Area of a triangle formed by 3 points (x1,y1), (x2,y2) and (x3,y3) is given by the following formula.

Area = $$\frac{|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|}{2}$$ ==> $$\frac{|2(6-2)+3(2-4)+5(4-6)|}{2}$$ = 4

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Re: What is the area of the triangle with points (2,4), (3,6), (5,2)?   [#permalink] 30 Sep 2017, 09:18
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