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If polygon ABCDE above has perimeter 26 and equilateral triangle BCD

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

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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

[Reveal] Spoiler:
Attachment:
2017-10-04_1125_003.png
2017-10-04_1125_003.png [ 6.48 KiB | Viewed 288 times ]
[Reveal] Spoiler: OA

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

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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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New post 05 Oct 2017, 04:10
This approach may help you......................
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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New post 09 Oct 2017, 16:45
Bunuel wrote:
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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

[Reveal] Spoiler:
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.

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