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

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New post 25 Feb 2019, 00:14
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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
#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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New post 25 Feb 2019, 12:49
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Bunuel wrote:
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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. \(\frac{x^ - xy}{2}\)


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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