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Re: What is the area of four sided figure formed by the intersection of [#permalink]

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09 Feb 2015, 04:37

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We need to find the equation |2X| + |Y| = 6

Equation 1 : 2X + Y = 6 which is Y = -2X + 6 . Points where this lines intersects the X and Y axis ( X = 0 , Y = 6 ) , ( X = 3 , Y = 0 ) Equation 2 : -2X - Y = 6 which is Y = -2X - 6 . Points where this lines intersects the X and Y axis ( X = 0 , Y = -6 ) , ( X = -3 , Y = 0 )

From here we know the intersects of the lines , Using area of triangles = 0.5 * X * Y = 0.5 * 3 * 6 = 9 Using symmetry 4 triangles = 9 * 4 = 36 . Answer is D . ( Sketch a diagram to visualize it helps !! )

Re: What is the area of four sided figure formed by the intersection of [#permalink]

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03 Jul 2016, 00:03

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These are four equations. If you carefully observe these equations because of the way mod functions are plotted around y and x axis as opposite images, these four lines form a rhombus with diagonals of lengths as 6 and 12 (if x =0 then possible y values 0,6 and 0,-6) and then (if y =0 x intercepts at 3,0 and -3,0. Area of rhombus is 1/2 * (product of diagonals) = 1/2 * 12 *6 = 36.

Re: What is the area of four sided figure formed by the intersection of [#permalink]

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24 Jul 2016, 22:29

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Turkish wrote:

What is the area of four sided figure formed by the intersection of the set of lines represented by |2x|+|y| = 6?

1. 18 2.24 3.30 4.36 5.48

we just need four XY pair to define the four-sided figure. Lets works with the concept of X and Y intercepts When |x|=0; then |y|=6 .. right y=-6 and 6 ; XY pairs are {0,-6} and {0,6}

when |y|=0 then |2x|= 6 x=-3 and 3 ; The XY pairs are (-3,0 and 3,0)

When you plot these XY pairs you will see that you get a diamond shaped figure (an upright RHOMBUS ) which can be divided into 2 equal triangles. the base of these two triangles is the x-axis

Now area of a triangle = 1/2 * base * height = 1/2 * 6*6 (the distance between -3 and 3 is 6) and the height is 6-0 = 6 Therefore Area of the triangle = \(\frac{1}{2}*36\) =====>18 There are 2 such triangle Total area = 2*18 =36 ANSWER IS D
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Last edited by LogicGuru1 on 05 Oct 2016, 12:41, edited 1 time in total.

Re: What is the area of four sided figure formed by the intersection of [#permalink]

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15 Aug 2016, 04:28

What's the fastest way to solve this?

I took almost 4 mins. First opened mods and found the 4 equations. Then found 2 points per equation. Then found area of one triangle and multiplied it by 4 (for area of the 4 triangles formed)

Re: What is the area of four sided figure formed by the intersection of [#permalink]

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30 Sep 2016, 06:23

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Turkish wrote:

What is the area of four sided figure formed by the intersection of the set of lines represented by |2x|+|y| = 6?

1. 18 2.24 3.30 4.36 5.48

took me some time to draw some points... but i believe the easiest way is: x=0, then y=6 or -6. y=0, x=3 or -3. we get 4 similar 90 degrees triangles, with the 90 degree angle at the origin. short leg is 3, long leg is 6. area is leg*leg/2 = 18/2 = 9. since we have 4 of these triangles, the area is 9*4 = 36.