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# Which of the following expresses the area of the shaded region in the

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
Which of the following expresses the area of the shaded region in the  [#permalink]

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25 Feb 2019, 00:14
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1
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Difficulty:

45% (medium)

Question Stats:

56% (01:37) correct 44% (02:27) wrong based on 18 sessions

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Which of the following expresses the area of the shaded region in the figure above?

A. $$\frac{x^2 - y^2}{2}$$

B. $$\frac{x^2 + y^2}{2}$$

C. $$x^2 - y^2$$

D. $$\frac{x^2 + xy}{2}$$

E. $$\frac{x^ - xy}{2}$$

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#GREpracticequestion Which of the following expresses the area of the shaded region in the figure above.jpg [ 30.21 KiB | Viewed 385 times ]

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Which of the following expresses the area of the shaded region in the  [#permalink]

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25 Feb 2019, 12:49
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Bunuel wrote:

Which of the following expresses the area of the shaded region in the figure above?

A. $$\frac{x^2 - y^2}{2}$$

B. $$\frac{x^2 + y^2}{2}$$

C. $$x^2 - y^2$$

D. $$\frac{x^2 + xy}{2}$$

E. $$\frac{x^ - xy}{2}$$

Attachment:
#GREpracticequestion Which of the following expresses the area of the shaded region in the figure above.jpg

Area shaded region = area big triangle - area small triangle

big triangle = 45-45-90 --> Therefore sides are in ration x:x:xrad(2)

area big triangle = .5x^2

Finding the area of small triangle is the tricky part:
- area = .5 base * height
- base small triangle = y
- height small triangle = ?????

- However, if we think of the two bases y & x as being parallel lines being cut by a transversal we can prove that the big triangle and the small triangle are similar triangles -----> This means the small triangle is also a 45-45-90 and therefore has a height of y

Therefore:
- area big triangle = .5x^2
- area small triangle = .5y^2

area shaded region = .5x^2 - .5y^2

Factoring out a .5 gives ---> answer choice A
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Which of the following expresses the area of the shaded region in the   [#permalink] 25 Feb 2019, 12:49
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