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# If polygon ABCDE above has perimeter 26 and equilateral triangle BCD

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Joined: 02 Sep 2009
Posts: 47157
If polygon ABCDE above has perimeter 26 and equilateral triangle BCD  [#permalink]

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05 Oct 2017, 01:41
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Difficulty:

15% (low)

Question Stats:

97% (01:18) correct 3% (00:00) wrong based on 30 sessions

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If polygon ABCDE above has perimeter 26 and equilateral triangle BCD has perimeter 18, what is the area of the rectangular region ABDE?

(A) 6
(B) 12
(C) 24
(D) 32
(E) 48

Attachment:

2017-10-04_1125_003.png [ 6.48 KiB | Viewed 698 times ]

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Re: If polygon ABCDE above has perimeter 26 and equilateral triangle BCD  [#permalink]

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05 Oct 2017, 02:09
1
Perimeter of polygon ABCDE = 26
Perimeter of equilateral triangle BCD = 18, so each side of triangle be of length 6
So BD=AC=6
subtracting AE, BC, CD from the perimeter of polygon ABCDE, we get AB + ED = 8, so AB=ED=4
Now the rectangle ABDE had length =6 and breadth = 4, so area of triangle ABDE = 6*4=24
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Re: If polygon ABCDE above has perimeter 26 and equilateral triangle BCD  [#permalink]

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05 Oct 2017, 04:10
Perimeter of polygon ABCDE = 26
Perimeter of equilateral triangle BCD = 18, so each side of triangle be of length 6
So BD=AC=6
subtracting AE, BC, CD from the perimeter of polygon ABCDE, we get AB + ED = 8, so AB=ED=4
Now the rectangle ABDE had length =6 and breadth = 4, so area of triangle ABDE = 6*4=24
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Re: If polygon ABCDE above has perimeter 26 and equilateral triangle BCD  [#permalink]

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09 Oct 2017, 16:45
Bunuel wrote:

If polygon ABCDE above has perimeter 26 and equilateral triangle BCD has perimeter 18, what is the area of the rectangular region ABDE?

(A) 6
(B) 12
(C) 24
(D) 32
(E) 48

Attachment:
2017-10-04_1125_003.png

Since equilateral triangle BCD has a perimeter of 18, each side is 6, which means that BC = CD = BD = 6. Furthermore, AE = 6 since AE = BD. If we let BA = DE = n, we can create the following equation to determine n:

BC + CD + DE + AE + AB = 26

6 + 6 + n + 6 + n = 26

2n = 8

n = 4

Thus, the area of rectangular region ABDE is 4 x 6 = 24.

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Re: If polygon ABCDE above has perimeter 26 and equilateral triangle BCD &nbs [#permalink] 09 Oct 2017, 16:45
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