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In the xy-coordinate plane, polygon APBCDA is formed by placing rectan

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Bunuel
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In the xy-coordinate plane, polygon APBCDA is formed by placing rectan [#permalink] New post   05 Jun 2020, 04:10
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In the xy-coordinate plane, polygon APBCDA is formed by placing rectangle ABCD and triangle APB as shown above. If sides AB and AD are parallel to the x- and the y- axes respectively, what is the area of polygon APBCDA?

(1) The coordinates of points A and C are (6, 8) and (12, 12) respectively
(2) The coordinates of point P are (8, 10)


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nick1816
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Re: In the xy-coordinate plane, polygon APBCDA is formed by placing rectan [#permalink] New post   05 Jun 2020, 06:44
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To find the area of shaded region, we need coordinates of ABCD or dimensions of ABCD and y- coordinates of P.

Statement 1 - It gives the coordinates of A, B, C and D. We have no idea about P.

Insufficient

Statement 2 - We have no idea about dimensions of rectangle ABCD.

Insufficient

Combining both statements, we can find the area of ABCD and triangle APB. We can find area of shaded region.

Sufficient


Bunuel wrote:

In the xy-coordinate plane, polygon APBCDA is formed by placing rectangle ABCD and triangle APB as shown above. If sides AB and AD are parallel to the x- and the y- axes respectively, what is the area of polygon APBCDA?

(1) The coordinates of points A and C are (6, 8) and (12, 12) respectively
(2) The coordinates of point P are (8, 10)


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Re: In the xy-coordinate plane, polygon APBCDA is formed by placing rectan [#permalink] New post   05 Jun 2020, 08:42
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IMO C

Stmt 1 gives A, C coordinates, we can find the other cordinates and length AB= 6, BC =4, Area of ABCD = 24. Since no details about P, cannott find area of APB Insufficient

Stmt2: Give P coordinates. Insufficient

Combine: Area for APB = 1/2 *base* height
Since P coordinates are available, height = 2, from Stmt 1 we know base = 6


area of polygon APBCDA = Area of ABCD - Area of APB

SUFFICIENT
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Re: In the xy-coordinate plane, polygon APBCDA is formed by placing rectan [#permalink] New post   06 Jun 2020, 07:20
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Sides AB and AD are parallel to the x- and the y-axes respectively

Statement 1 = A and C coordinates are given
Hence Coordinates of A, B, C and D are concluded as sides are parallel to axes. But it still does not help us find the area of triangle.

so INSUFFICIENT

Statement 2 = Only coordinates of P are given.
Alone it cannot tell us much about the area of the rectangle.

So INSUFFICIENT

Combine both statements, and we can get the area of rectangle and the triangle. Thus we can get the area of shaded figure.

HENCE C
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Re: In the xy-coordinate plane, polygon APBCDA is formed by placing rectan [#permalink] New post   06 Jun 2020, 12:02
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From Statement 1:
Given coordinates are A (6,8) and C (12,12)
Hence B and D can be calculated as (12,8) and (6,12) respectively;
here we can get area of rect. ABCD.
Not Polygon APBCDA,
So,
INSUFFICIENT

Now from statement 2:
Coordinate of P is given as (8,10)
Here nothing we can get.
So, again
INSUFFICIENT

Combining both statements we can calculate area of Triangle APB;
and previously we obtained area of rect. ABCD.
Thus area can be measured easily.
So, Combining
SUFFICIENT

Hence option C.
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Re: In the xy-coordinate plane, polygon APBCDA is formed by placing rectan [#permalink] New post   07 Jun 2020, 05:07
Bunuel wrote:

In the xy-coordinate plane, polygon APBCDA is formed by placing rectangle ABCD and triangle APB as shown above. If sides AB and AD are parallel to the x- and the y- axes respectively, what is the area of polygon APBCDA?

(1) The coordinates of points A and C are (6, 8) and (12, 12) respectively
(2) The coordinates of point P are (8, 10)


C, IMO

(1) The coordinates of points A and C are (6, 8) and (12, 12) respectively

No info about point P . SO insufficient .

(2) The coordinates of point P are (8, 10)

No Info about point A and C . Not sufficient .

Combining statement 1 and 2 we can find the height of the triangle and the area of the triangle and the polygon respectively
So sufficient .

Hence C is the ans .
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Re: In the xy-coordinate plane, polygon APBCDA is formed by placing rectan [#permalink]
07 Jun 2020, 05:07
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Bunuel
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