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The figure shows rectangle ABCD with area 60 cm^2

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MathRevolution
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The figure shows rectangle ABCD with area 60 cm^2 [#permalink] New post   15 Nov 2019, 01:46
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[GMAT math practice question]

The figure shows rectangle \(ABCD\) with area \(60 cm^2\). The rectangle is divided by the \(4\) congruent rectangles, and \(BD\) is a diagonal of rectangle \(ABCD\). What is the area of the shaded region?

Attachment:
11.15.png
11.15.png [ 14.5 KiB | Viewed 1338 times ]


A. \(11\)

B. \(13\)

C. \(15\)

D. \(16\)

E. \(17\)
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C
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Re: The figure shows rectangle ABCD with area 60 cm^2 [#permalink] New post   15 Nov 2019, 01:51
required shaded portion is equal to one strip on the rectangule and one strip is equal to 1/4 of area (by symmetry)
reqd area=1/4*60 =15

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The figure shows rectangle ABCD with area 60 cm^2 [#permalink] New post   15 Nov 2019, 12:34
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MathRevolution wrote:
[GMAT math practice question]

The figure shows rectangle \(ABCD\) with area \(60 cm^2\). The rectangle is divided by the \(4\) congruent rectangles, and \(BD\) is a diagonal of rectangle \(ABCD\). What is the area of the shaded region?

Attachment:
The attachment 11.15.png is no longer available


A. \(11\)

B. \(13\)

C. \(15\)

D. \(16\)

E. \(17\)

Attachment:
GMAT PS.png
GMAT PS.png [ 13.81 KiB | Viewed 1235 times ]


Let each rectangle have width \(x\) and length \(y \)
so \(4x*y\) = 60 or \(xy\) = 15 this is the area of each rectangle.
Now BDC is a triangle with base \(4x\) and height \(y\) hence area of triangle BDC = \(\frac{1}{2}\)\(*{4xy }=30\) ( \(4xy=60\) )
Now area of shaded region is area of triangle BDC - area of one rectangle.
Area of triangle BDC = 30 , Area of one rectangle ( Portion in red ) =15
Hence:30-15= 15
Ans- C
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Re: The figure shows rectangle ABCD with area 60 cm^2 [#permalink] New post   17 Nov 2019, 18:43
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=>

The area of the shaded region is half of the area of rectangle \(EFGH\).

The area of rectangle \(EFGH\) is half of the area of rectangle \(ABCD, 60.\)

So the area of the shaded region is \((\frac{1}{2})(\frac{1}{2})(60) = 15.\)

Therefore, the answer is C.
Answer: C
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Re: The figure shows rectangle ABCD with area 60 cm^2 [#permalink]
17 Nov 2019, 18:43
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