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

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
What is the area of the shaded region in the figure above ?  [#permalink]

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20 Nov 2015, 01:43
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Difficulty:

5% (low)

Question Stats:

92% (01:08) correct 8% (01:29) wrong based on 197 sessions

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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

Attachment:

Untitled.png [ 1.44 KiB | Viewed 6093 times ]

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Joined: 09 Feb 2015
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What is the area of the shaded region in the figure above ?  [#permalink]

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20 Nov 2015, 02:21
Answer: 57, 8*9 - 6*3 + (1/2*2*3) = 72 - 18 + 3 = 57
Director
Joined: 20 Feb 2015
Posts: 760
Concentration: Strategy, General Management
Re: What is the area of the shaded region in the figure above ?  [#permalink]

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20 Nov 2015, 03:11
area of the shaded region apart from the 6 to 9 additional trapezium
= 6*8=48
area of trapezium =h(s1+s2)/2=3*(4+2)/2=9
total area=48+9=57
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Posts: 4018
Re: What is the area of the shaded region in the figure above ?  [#permalink]

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20 Nov 2015, 07:07
1
Bunuel wrote:

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

Attachment:
Untitled.png

Area of shaded region = (area of large 8 x 9 rectangle) - (area of unshaded trapezoid)
= (72) - (4 + 6)(3)/2
= 71 - 15
= 57
= B

For info on finding the area of a trapezoid see this free video - http://www.gmatprepnow.com/module/gmat- ... /video/874 (starting at 4:05)\

Cheers,
Brent
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Re: What is the area of the shaded region in the figure above ?  [#permalink]

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20 Nov 2015, 10:31
Bunuel wrote:

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

Attachment:
The attachment Untitled.png is no longer available

I am dividing the figure into 4 parts.

A - A rectangle with length 6 and breadth 4
B - A rectangle with length 6 and breadth 4

C - A rectangle with length 3 and breadth 2

D - A triangle with Base 2 and Height 3

Area of the entire figure = Area of A + Area of B + Area of C + Area of D

Area of A = 24
Area of B = 24
Area of C = 6
Area of D = 3

Total Area of the entire figure = 57 (24 + 24 + 6 + 3)

Attachments

Untitled.png [ 2.48 KiB | Viewed 4804 times ]

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Joined: 03 Aug 2016
Posts: 40
Re: What is the area of the shaded region in the figure above ?  [#permalink]

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09 Apr 2018, 11:09
Bunuel wrote:

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

Attachment:
Untitled.png

Here's another way to do this problem:

Area of shaded region = Area of square - area of unshaded region (trapezoid, in this case)

Area of square = B*H --> 8*9 = 72

Area of unshaded region = (B1+B2)/2 *H --> (6+4)/2 * 3 =15

Area of shaded region = 72-15 = 57
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Re: What is the area of the shaded region in the figure above ?   [#permalink] 09 Apr 2018, 11:09
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