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505-555 Level|   Geometry|      
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In the figure above, square PQRS is divided into four smaller squares. Updated on: 15 Jul 2019, 03:58
Originally posted by Bunuel on 19 Sep 2017, 23:29.
Last edited by Sajjad1994 on 15 Jul 2019, 03:58, edited 1 time in total.
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A
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87% (01:15) correct 13% (01:58) wrong based on 47 sessions

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In the figure above, square PQRS is divided into four smaller squares. If the area of the shaded region is 3, what is the area of PQRS?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 1

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2017-09-20_1018.png
2017-09-20_1018.png [ 5.24 KiB | Viewed 4782 times ]
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A
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In the figure above, square PQRS is divided into four smaller squares. 19 Sep 2017, 23:33
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4 smaller Equal squares?

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In the figure above, square PQRS is divided into four smaller squares. 19 Sep 2017, 23:35
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4 smaller Equal squares?

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If a square is divided into 4 smaller squares as shown above, could these four squares not be equal?
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In the figure above, square PQRS is divided into four smaller squares. Updated on: 20 Sep 2017, 00:21
Originally posted by Octobre on 19 Sep 2017, 23:35.
Last edited by Octobre on 20 Sep 2017, 00:21, edited 1 time in total.
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If yes I would say answer A
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In the figure above, square PQRS is divided into four smaller squares. Updated on: 20 Sep 2017, 00:22
Originally posted by Octobre on 19 Sep 2017, 23:39.
Last edited by Octobre on 20 Sep 2017, 00:22, edited 1 time in total.
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Bunuel
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4 smaller Equal squares?

If a square is divided into 4 smaller squares as shown above, could these four squares not be equal?
True they have to
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In the figure above, square PQRS is divided into four smaller squares. 19 Sep 2017, 23:48
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In the figure, square PQRS is divided into four smaller squares.
=> Considering all the 4 smaller squares are equal in size.

If the area of the shaded region is 3, what is the area of PQRS?

= > In figure, 2 sides of shaded region : PR is diagonal and other end is center of 2 sides. If we check shaded region consist of 3 triangles. And Square can be divided into kind of 8 triangles out of which shaded region is 3 triangles.

So if area of square is 8x than of shaded region is 3x.

Given Area of shaded reason is 3 => Area of square = 8

Answer: A
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In the figure above, square PQRS is divided into four smaller squares. 20 Sep 2017, 11:42
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Bunuel

In the figure above, square PQRS is divided into four smaller squares. If the area of the shaded region is 3, what is the area of PQRS?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 1

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Attachment:
2017-09-20_1018.png

Area of the shaded region is 3
The shaded region consists of 3 triangles
Hence area of each triangle is 1, since all triangles are similar.
Now, considering the entire square, it consists of 8 such triangles,
hence area of square PQRS = 8
Answer A.

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In the figure above, square PQRS is divided into four smaller squares. 23 Sep 2017, 13:12
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Bunuel

In the figure above, square PQRS is divided into four smaller squares. If the area of the shaded region is 3, what is the area of PQRS?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 1

Show Spoiler
Attachment:
2017-09-20_1018.png
A simple ratio can be used.

Divide the fourth small square (with vertex S) in half like the other small squares.

The large square has 8 triangles. Three of the 8 triangles are shaded.

So \(\frac{3}{8}\) of PQRS is shaded, or

The shaded region = \(\frac{3}{8}A\) of PQRS

The shaded region also = area of 3

Set them equal

\(\frac{3}{8}A\) = 3

\(A = 8\)

ANSWER A
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