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What is the area of the shaded region in the figure above?

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Joined: 02 Sep 2009
Posts: 43381
What is the area of the shaded region in the figure above? [#permalink]

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New post 17 Dec 2017, 22:13
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

92% (00:45) correct 8% (00:12) wrong based on 36 sessions

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Image
What is the area of the shaded region in the figure above?

(A) 72
(B) 57
(C) 55
(D) 54 1/2
(E) 49 1/2

[Reveal] Spoiler:
Attachment:
2017-12-18_1010.png
2017-12-18_1010.png [ 9.8 KiB | Viewed 548 times ]
[Reveal] Spoiler: OA

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What is the area of the shaded region in the figure above? [#permalink]

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New post 17 Dec 2017, 22:48
Bunuel wrote:
Image
What is the area of the shaded region in the figure above?

(A) 72
(B) 57
(C) 55
(D) 54 1/2
(E) 49 1/2

[Reveal] Spoiler:
Attachment:
2017-12-18_1010.png


Area of the shaded region in the figure= Area of the region(Rectangle) - Area of unshaded region(trapezium)

Area of rectangle = 8*9 =72

Area of trapezium = (a+b/2)*h = (10/2)*3 = 15

72-15= 57

Hence B

*Corrected Typo*
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Re: What is the area of the shaded region in the figure above? [#permalink]

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New post 17 Dec 2017, 23:44
An easy one to solve.
Multiple methods to solve such problems

1.Area of shaded region = Area of rectangle - Area of trapezium(unshaded)
2.Area of shaded region = Area of rectangle - [Area of small rectangle + Area of triangle](unshaded)

1. Area of shaded region = 8*9 - 1/2*(6+4)*3 = 72 - 15 = 57
2. Area of shaded region = 8*9 - [4*3 + 1/2*2*3] = 72 - [12+3] = 57

Option B.

Kudos if it helps :)
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Re: What is the area of the shaded region in the figure above? [#permalink]

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New post 18 Dec 2017, 00:18
Bunuel wrote:
Image
What is the area of the shaded region in the figure above?

(A) 72
(B) 57
(C) 55
(D) 54 1/2
(E) 49 1/2

[Reveal] Spoiler:
Attachment:
2017-12-18_1010.png


Note that the slanting line has end points at (4, 6) and (6, 9).
Area of the trapezium so formed = (1/2)*3*(4 + 2) = 9

Area of the rest of the shaded rectangle = 6*8 = 48

Total shaded area = 9 + 48 = 57

Answer (B)
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Re: What is the area of the shaded region in the figure above?   [#permalink] 18 Dec 2017, 00:18
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