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What is the area of quadrilateral ABCD?
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01 Feb 2019, 11:36
01 Feb 2019, 11:36
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Question Stats:
55% (01:42) correct
44% (02:18) wrong based on 67 sessions
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What is the area of quadrilateral ABCD?
#GREpracticequerstion What is the area of quadrilateral ABC.jpg [ 20.15 KiB | Viewed 9768 times ]
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#GREpracticequerstion What is the area of quadrilateral ABC.jpg [ 20.15 KiB | Viewed 9768 times ]
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38
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What is the area of quadrilateral ABCD?
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06 Feb 2019, 12:17
06 Feb 2019, 12:17
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Carcass wrote:
What is the area of quadrilateral ABCD?
Attachment:
#GREpracticequerstion What is the area of quadrilateral ABC.jpg
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38
Since this is an odd-shaped quadrilateral, there's no convenient area formula we can apply here.
Instead, let's add an extra line to divide the quadrilateral into two TRIANGULAR regions.
Let's find the area of Region #1 first
If we make side AB the base of the triangle, then the height = 10
Area of triangle = (base)(height)/2 = (6)(10)/2 = 30
Now, we'll find the area of Region #2
If we make side AD the base of the triangle, then the height = 4
Area of triangle = (base)(height)/2 = (4)(4)/2 = 8
We get:
TOTAL area of quadrilateral ABCD = 30 + 8 = 38
Answer: 38
Cheers,
Brent
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Re: What is the area of quadrilateral ABCD?
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06 Feb 2019, 18:40
06 Feb 2019, 18:40
3
Expert Reply
Carcass wrote:
What is the area of quadrilateral ABCD?
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The attachment #GREpracticequerstion What is the area of quadrilateral ABC.jpg is no longer available
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38
Another way is to convert it into a rectangle by extending as shown in the sketch.
Area of quadrilateral is the area of rectangle-areas of two triangle..
Area of the rectangle = \((11-1)*(7-1)=10*6=60\).
Area of the triangle DCF = \(\frac{1}{2}*(11-5)(5-1)=3*4=12\)
Area of the triangle BCE = \(\frac{1}{2}*(11-1)(7-5)=10\)
Hence area of quadrilateral ABCD = 60-12-10=38
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#GREpracticequerstion What is the area of quadrilateral ABC.jpg [ 14.76 KiB | Viewed 9637 times ]
