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PQRS is a parallelogram and ST = TR. What is the ratio of the area of

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Joined: 02 Sep 2009
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PQRS is a parallelogram and ST = TR. What is the ratio of the area of  [#permalink]

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16 May 2016, 02:33
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25% (medium)

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79% (01:09) correct 21% (01:10) wrong based on 174 sessions

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PQRS is a parallelogram and ST = TR. What is the ratio of the area of triangle QST to the area of the parallelogram?

A. 1 : 2
B. 1 : 3
C. 1 : 4
D. 1 : 5
E. it cannot be determined

Attachment:

2016-05-16_1331.png [ 1.64 KiB | Viewed 4489 times ]

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Posts: 6793
Re: PQRS is a parallelogram and ST = TR. What is the ratio of the area of  [#permalink]

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16 May 2016, 06:20
Bunuel wrote:

PQRS is a parallelogram and ST = TR. What is the ratio of the area of triangle QST to the area of the parallelogram?

A. 1 : 2
B. 1 : 3
C. 1 : 4
D. 1 : 5
E. it cannot be determined

Attachment:
2016-05-16_1331.png

The diagonal of llgm divides the AREA in two equal parts..
so SQ divides the area in two equal parts ..
AREA of QRS = 1/2 of PQRS..

Now in QSR, QT divides the triangle QST in two equal areas,
Because the height of QST ans QRT is SAME and it is given that the BASE in both cases ST and TR are also same ...
SO Area of QST = Area of RST...
so AREA of QST = $$\frac{1}{2}$$of QST = $$\frac{1}{2}$$of $$\frac{1}{2}$$of llgm PQRS $$= \frac{1}{4}$$
ans C
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Re: PQRS is a parallelogram and ST = TR. What is the ratio of the area of  [#permalink]

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16 May 2016, 10:30
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Bunuel wrote:

PQRS is a parallelogram and ST = TR. What is the ratio of the area of triangle QST to the area of the parallelogram?

A. 1 : 2
B. 1 : 3
C. 1 : 4
D. 1 : 5
E. it cannot be determined

Attachment:
2016-05-16_1331.png

Given ST = TR ; so T must be the midpoint of SR

Area of Δ SQT = Δ QTR

Further ; Area of Δ PSQ = Area of Δ QSR ( Since the parallelogram is made up of 2 equal triangles)

So we may say that the parallelogram is made up of the area of 4 equal Δs of area QST

So, the //gm PQRS = 4 Δ QST

Hence the ratio of the area of triangle QST to the area of the parallelogram = 1 : 4 ; answer will be (C)
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Re: PQRS is a parallelogram and ST = TR. What is the ratio of the area of  [#permalink]

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16 May 2016, 13:15
Area of the parallelogram is = perpendicular * base (SR)
Area of the triangle is = (1/2) * perpendicular * base (ST) = (1/2) * perpendicular * SR/2

Ratio = 1/4. C

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Re: PQRS is a parallelogram and ST = TR. What is the ratio of the area of  [#permalink]

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07 Sep 2018, 15:09
Top Contributor
Bunuel wrote:

PQRS is a parallelogram and ST = TR. What is the ratio of the area of triangle QST to the area of the parallelogram?

A. 1 : 2
B. 1 : 3
C. 1 : 4
D. 1 : 5
E. it cannot be determined

Attachment:
2016-05-16_1331.png

Since ST = TR, let's let x = each length

Also, let's say the parallelogram has height h

So, the length of the parallelogram's base = x + x = 2x
Area of a PARALLELOGRAM = (base)(height)
= (2x)(h)
= 2xh

Now let's determine the area of triangle QST

Area of any triangle = (base)(height)/2
So, area of triangle QST = xh/2

What is the ratio of the area of triangle QST to the area of the parallelogram?

Looks like we need to simplify our ratio.
Take: xh/2 : 2xh
Divide both sides by xh to get: 1/2 : 2_
Multiply both sides by 2 to get: 1 : 4

Cheers,
Brent
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Re: PQRS is a parallelogram and ST = TR. What is the ratio of the area of &nbs [#permalink] 07 Sep 2018, 15:09
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