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

Question

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

GMATinsight · Answer

Answer: Option A

Hint: Draw the figure and then judge the figure

Swaroopdev · Answer

GMATinsight

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

GMATinsight · Answer

Thank you. Have made correction...

chetan2u · Answer

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

Bunuel · Answer

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) .

Fdambro294 · Answer

Strategy used to approach a weird quadrilateral when you are not sure about the Lengths of the Sides:

Fill in the Extra "Parts" to make it a Rectangle or Square with 90 Degree Perpendicular Angles

Area of Quadrilateral in question = 
(Area of your Created Rectangle) - (Parts, which usually consist of Right Triangles, that are NOT part of the Quadrilateral in question)

In addition to the Points Given, Fill in the following Points in order to Create our Rectangle:

Point (15 , 6) --------> and connect a Straight Horizontal Line from (2 , 6) to (15 , 6) that has Length of 13 Units

and

Point (2 , -4) -------> and connect a Straight Horizontal Line from (15 , -4) to (2 , -4) that has Length of 13 Units

if done correctly, you know have 2 Right Triangles that you added to the Given Quadrilateral in the Question and this Comes together to form a RECTANGLE

I. Area of Created Rectangle

13 Units = Length (as shown above)

Width = (Y-Coordinate of Point (15 , 6) ) - (Y-Coordinate of Point (15 , -4) = 10 Units

Area of Created Rectangle = 13 * 10 = 130 Units

II. Area of 2 Right Triangles

(1st) The Right Triangle on the Bottom of the Created Rectangle with Points:
(2 , -2) ----- (2 , -4) ------ (15 , -4)

will have Leg = 13 and Leg = 2

Area = (1/2) * 2 * 13 = 13 Units

(2nd) the Right Triangle on the Top of the Created Rectangle with Points:
(2 , 6) ------ (15 , 6) ------ (15 , 2)

will have Leg = 13 and Leg = 4

Area = (1/2) * 4 * 13 = 26

Finally, the Area of the Quadrilateral in question is equal to:

(130) - (13) - (26) = 91

-A- is the correct Answer

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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

Prep Toolkit

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