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In a rectangular coordinate system, what is the area of a quadrilatera

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In a rectangular coordinate system, what is the area of a quadrilatera  [#permalink]

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New post 08 Jul 2015, 03:37
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In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,-2), (2, 6), (15, 2), (15,-4)?

A. 91
B. 95
C. 104
D. 117
E. 182

Kudos for a correct solution.

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In a rectangular coordinate system, what is the area of a quadrilatera  [#permalink]

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New post Updated on: 10 Jul 2015, 06:02
1
Bunuel wrote:
In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,-2), (2, 6), (15, 2), (15,-4)?

A. 91
B. 95
C. 104
D. 117
E. 182

Kudos for a correct solution.


Answer: Option A

Hint: Draw the figure and then judge the figure
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Originally posted by GMATinsight on 08 Jul 2015, 04:05.
Last edited by GMATinsight on 10 Jul 2015, 06:02, edited 1 time in total.
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Re: In a rectangular coordinate system, what is the area of a quadrilatera  [#permalink]

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New post 10 Jul 2015, 05:54
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GMATinsight

Your answer says option B as the answer, must be a typo. just letting you know.
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Re: In a rectangular coordinate system, what is the area of a quadrilatera  [#permalink]

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New post 10 Jul 2015, 06:02
Swaroopdev wrote:
GMATinsight

Your answer says option B as the answer, must be a typo. just letting you know.


Thank you. Have made correction... :)
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Re: In a rectangular coordinate system, what is the area of a quadrilatera  [#permalink]

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New post 10 Jul 2015, 07:56
2
Bunuel wrote:
In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,-2), (2, 6), (15, 2), (15,-4)?

A. 91
B. 95
C. 104
D. 117
E. 182

Kudos for a correct solution.


looking at the coord, one can see that the quad has only two sides parallel , so its a trapezium...
the two parallel sides are (6+2)and (2+4)..
the distance between the two llel lines is 15-2=13..
area of trap=(8+6)*13/2=91
ans A
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Re: In a rectangular coordinate system, what is the area of a quadrilatera  [#permalink]

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New post 13 Jul 2015, 02:39
2
2
Bunuel wrote:
In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,-2), (2, 6), (15, 2), (15,-4)?

A. 91
B. 95
C. 104
D. 117
E. 182

Kudos for a correct solution.


800score Official Solution:

First, we should make a rough sketch of the figure to determine its general shape. Its left side and right side are parallel, with the left side having a length of 8 and the right side having a length of 6. The distance between these two sides is 13.This figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:

Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.

We can now determine the area of the quadrilateral:

Area = 1/2 × (8 + 6) × 13 = 1/2 × 14 × 13 = 7 × 13 = 91.

The correct answer is choice (A).

Alternate Method (Breaking the figure apart):
Without the formula for the area of a trapezoid, we can still solve the problem. We can draw two horizontal lines through the figure, one at y = 2 and one at y = -2 to divide the trapezoid
into an upper triangle, a rectangle, and a lower triangle.

The upper triangle has an area of (1/2) × 4 × 13 = 26.
The rectangle has an area of 4 × 13 = 52.
The lower triangle has an area of 1/2 × 2 × 13 = 13.

Adding these areas, we get the area for the quadrilateral:
52 + 26 + 13 = 91.

Again, we see that the correct answer is choice (A).
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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In a rectangular coordinate system, what is the area of a quadrilatera  [#permalink]

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