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# In the figure, ABCD is a rectangle and E is a point on the side AB. If

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In the figure, ABCD is a rectangle and E is a point on the side AB. If  [#permalink]

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09 Oct 2018, 22:29
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Difficulty:

15% (low)

Question Stats:

91% (01:02) correct 9% (00:24) wrong based on 13 sessions

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In the figure, ABCD is a rectangle and E is a point on the side AB. If AB = 10 and AD = 5, what is the area of the shaded region in the figure?

(A) 25

(B) 30

(C) 35

(D) 40

(E) 45

Attachment:

rectangle.jpg [ 29.54 KiB | Viewed 349 times ]

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In the figure, ABCD is a rectangle and E is a point on the side AB. If  [#permalink]

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10 Oct 2018, 00:48
Bunuel wrote:

In the figure, ABCD is a rectangle and E is a point on the side AB. If AB = 10 and AD = 5, what is the area of the shaded region in the figure?

(A) 25

(B) 30

(C) 35

(D) 40

(E) 45

Attachment:
rectangle.jpg

PROPERTY: The area of Triangle DEC will always be half of area of Rectangle ABCD irrespective of where the point E on line AB is. This is because of simple fact that Area of rectangle $$ABCD = l*b$$ and Area of Triangle $$DEC = (1/2)*l*b$$

i.e. area of shaded region = area of unshaded region $$= (1/2)*AB*AD = (1/2)*10*5 = 25$$

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In the figure, ABCD is a rectangle and E is a point on the side AB. If   [#permalink] 10 Oct 2018, 00:48
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