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Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS?

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Bunuel
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Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS? [#permalink] New post   05 Oct 2020, 03:45
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Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS?


(1) The coordinates of point P are (2.0), and the coordinates of point R are (8,2).
(2) The coordinates of point S are (6.0).
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C
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Re: Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS? [#permalink] New post   05 Oct 2020, 04:56
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Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS?

Explanation: Clearly Quadrilateral PQRS is a parallelogram with PQ||RS and QR||P5

(S1) The coordinates of point P are (2.0), and the coordinates of point R are (8,2).
Not enough information about remaining two vertices coordinate orside lengths.

Hence S1 is insufficient.

(S2) The coordinates of point S are (6.0).
Not enough information about remaining three vertices coordinate orside lengths.

Hence S2 is insufficient.

Combining S1 and S2
Now we have 3 vertices P(2,0) S(6,0) R(8,2) and Q(x,y)

now for parallelogram PQRS PQ=RS=2√2 and PS=QR=4

and height h=(2√2 )^2-2^2 (draw a perpendicular from R and apply Pythagoras)
i.e h=2

area Parallelogram PQRS= base*height
=PS*2
=4*2
=8

Hence C is the correct answer IMO
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Quadrilateral PQRS has PQ||RS and QR||PS. What is the area of PQRS? [#permalink] New post   09 Oct 2020, 02:44
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Given a parallelogram. Area = height * length

(1) The coordinates of point P are (2,0), and the coordinates of point R are (8,2).
Point Q and S can change and hence change the height and length.
not sufficient.
(2) The coordinates of point S are (6,0).
Not sufficient.

Combine: P, R, S are fixed. Q will also get fixed given PQRS is a parallelogram
So, Sufficient.
IMO, C
----------------------------------------------------------------------------------------

Not necessarily but if you wish to solve:
Take PS as a length. PS = 4
Height =2 [coordinates of R- (8,2)]
So, area = 8
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Re: Quadrilateral PQRS has PQ||RS and QR||PS. What is the area of PQRS? [#permalink] New post   09 Oct 2020, 07:07
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Bunuel wrote:
Quadrilateral PQRS has PQ||RS and QR||PS. What is the area of PQRS?


(1) The coordinates of point P are (2.0), and the coordinates of point R are (8,2).

(2) The coordinates of point S are (6.0).


(1) insufic
(2) insufic
(1/2) sufic
we have parallelogram with height 2 and base 4
(C)
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Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS? [#permalink] New post   09 Oct 2020, 11:10
Akp880 wrote:
Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS?

Explanation: Clearly Quadrilateral PQRS is a parallelogram with PQ||RS and QR||P5

(S1) The coordinates of point P are (2.0), and the coordinates of point R are (8,2).
Not enough information about remaining two vertices coordinate orside lengths.

Hence S1 is insufficient.

(S2) The coordinates of point S are (6.0).
Not enough information about remaining three vertices coordinate orside lengths.

Hence S2 is insufficient.

Combining S1 and S2
Now we have 3 vertices P(2,0) S(6,0) R(8,2) and Q(x,y)

now for parallelogram PQRS PQ=RS=2√2 and PS=QR=4

and height h=(2√2 )^2-2^2 (draw a perpendicular from R and apply Pythagoras)
i.e h=2

area Parallelogram PQRS= base*height
=PS*2
=4*2
=8

Hence C is the correct answer IMO


I got it right... by guessing, but I was very lost starting at "now for parallelogram PQRS PQ=RS=2√2 and PS=QR=4."
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Re: Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS? [#permalink] New post   15 Oct 2020, 03:05
option A, B and D are out as 1 and 2 are not sufficient...Now if you combine 1 and 2, you will see PS lies on the x axis and distance between P and S is 4, Now if you see a triangle PRS you know the base i.e. 4 (PS) and height too(2) (as y coordinate of R is 2), so you know the area of triangle PRS (1/2)(4)(2) = 4. Now, PR is nothing but the diagonal of the parallelogram PQRS, so overall area of the parallelogram will be twice of the area of triangle PRS => 8. Therefore C is sufficient.

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Re: Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS? [#permalink] New post   31 Jan 2022, 23:39
exc4libur wrote:
Bunuel wrote:
Quadrilateral PQRS has PQ||RS and QR||PS. What is the area of PQRS?


(1) The coordinates of point P are (2.0), and the coordinates of point R are (8,2).

(2) The coordinates of point S are (6.0).


(1) insufic
(2) insufic
(1/2) sufic
we have parallelogram with height 2 and base 4
(C)


exc4libur
On what basis it is confirmed that diagram is parallelogram.
Since it is given in questiont that lines are parallel we cannot say its parallelogram. Parallelogram opposite side is equal and parallel. How it is determined opposite sides are equal.
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Re: Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS? [#permalink] New post   17 Feb 2023, 07:07
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Re: Quadrilateral PQRS has PQ||RS and QR||P5. What is the area of PQRS? [#permalink]
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