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555-605 Level|   Geometry|      
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Bunuel
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The area of parallelogram ABCD equals 08 Mar 2023, 09:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

73% (01:33) correct 27% (01:33) wrong based on 37 sessions

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The area of parallelogram ABCD equals


(A) 6
(B) 7.5
(C) \(5 \sqrt{3}\)
(D) 12
(E) 15


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Attachment:
1.jpg
1.jpg [ 26.54 KiB | Viewed 2582 times ]
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D
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SaquibHGMATWhiz
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GMAT 1: 760 Q51 V40
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The area of parallelogram ABCD equals 11 Apr 2023, 05:42
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Bunuel
The area of parallelogram ABCD equals
(A) 6
(B) 7.5
(C) \(5 \sqrt{3}\)
(D) 12
(E) 15
Show more
Solution:

  • We have 2 right angle triangles with hypotenuse 5 and one of the other side as 3
  • This means the third side will be 4 (3, 4, 5 is a Pythagorean triplet)
    Attachment:
    pytha.png
    pytha.png [ 27.16 KiB | Viewed 1699 times ]

  • Area of parallelogram ABCD = Area of ABD + Area of BCD
    \(=(1/2*BA*BD)+(1/2*DC*BD)\)
    \(=(1/2*3*4)+(1/2*3*4)\)
    \(=12\)

Hence the right answer is Option D
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prachisaraf
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The area of parallelogram ABCD equals 11 Apr 2023, 10:12
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Getting D as the answer too. Does the OA needs to be changed ?
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Bunuel
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The area of parallelogram ABCD equals 13 Apr 2023, 01:30
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prachisaraf
Getting D as the answer too. Does the OA needs to be changed ?
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Yes. Edited the OA. Sorry for the confusion and thank you for reporting!
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The area of parallelogram ABCD equals 13 Apr 2023, 03:40
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Bunuel

The area of parallelogram ABCD equals


(A) 6
(B) 7.5
(C) \(5 \sqrt{3}\)
(D) 12
(E) 15


Show Spoiler
Attachment:
1.jpg
Show more

Since AB || CD in a parallelogram, the diagonal BD is a transversal and the will have equal interior alternate angles. So angle ABD = angle CDB = 90 degrees.

In right triangle ABD, recognise that the hypotenuse AD is 5 and one leg is 3 so the other leg must be 4 (3-4-5 triangle).
Area of this triangle = (1/2)*3*4 = 6

Since opposite sides are equal and parallel in a parallelogram, area of triangle BCD is also 6.

Area of parallelogram = area of triangle ABD + area of triangle BCD = 6 + 6 = 12

Answer (D)
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