It is currently 14 Dec 2017, 05:26

# Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The hexagon ABCDEF is regular. That means all its sides are the same l

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42606

Kudos [?]: 135613 [0], given: 12705

The hexagon ABCDEF is regular. That means all its sides are the same l [#permalink]

### Show Tags

05 Nov 2017, 00:37
00:00

Difficulty:

(N/A)

Question Stats:

71% (01:20) correct 29% (02:07) wrong based on 14 sessions

### HideShow timer Statistics

The hexagon ABCDEF is regular. That means all its sides are the same length and all its interior angles are the same size. Each side of the hexagon is 2 feet. What is the area of the rectangle BCEF?

(A) 4 square feet

(B) $$4\sqrt{3}$$ square feet

(C) 8 square feet

(D) $$4 + 4\sqrt{3}$$ square feet

(E) 12 square feet

[Reveal] Spoiler:
Attachment:

2017-11-05_1232.png [ 5.8 KiB | Viewed 551 times ]
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135613 [0], given: 12705

VP
Joined: 22 May 2016
Posts: 1126

Kudos [?]: 402 [0], given: 645

The hexagon ABCDEF is regular. That means all its sides are the same l [#permalink]

### Show Tags

05 Nov 2017, 07:32
Bunuel wrote:

The hexagon ABCDEF is regular. That means all its sides are the same length and all its interior angles are the same size. Each side of the hexagon is 2 feet. What is the area of the rectangle BCEF?

(A) 4 square feet

(B) $$4\sqrt{3}$$ square feet

(C) 8 square feet

(D) $$4 + 4\sqrt{3}$$ square feet

(E) 12 square feet

[Reveal] Spoiler:
Attachment:
The attachment 2017-11-05_1232.png is no longer available

Attachment:

hhhh.png [ 12.04 KiB | Viewed 410 times ]

Rectangle width
Connect sides BF and CE of the rectangle

All sides of the hexagon have length 2 feet. Width of rectangle BCEF = 2 feet

Rectangle length

Create two right triangles at angle D

Draw a perpendicular bisector from angle D to opposite side EC

A regular hexagon has internal angle measures of 120 degrees:
(n-2)(180) = 720 degrees total, divided by 6 angles = 120 each

Angle D is bisected into 120/2 = two angles of 60°, so

angle CDX = 60
Angle DXC = 90
Angle DCX = 30
--Either: Angle DCB = 120. Rectangle vertex BCE = 90, so (120 - 90) = 30; or
--Two of the angles in Δ DCX total 150; (180- 150) = 30

There are now two identical right 30-60-90 triangles: Δ DEX and Δ DCX

30-60-90 right triangles have side lengths in ratio $$x: x\sqrt{3}: 2x$$

Side DE, opposite the 90° angle, corresponds with $$2x$$ and = $$2$$
Side DX, opposite the 30° angle, corresponds with $$x$$ and therefore = $$1$$
Side EC, opposite the 60° angle, corresponds with $$x\sqrt{3}$$ and therefore $$= \sqrt{3}$$

The two right 30-60-90 triangles are identical; the length of the rectangle is the sum of their sides of $$\sqrt{3}$$
Length of rectangle: $$2\sqrt{3}$$

Area of rectangle

$$Area = (L * W) = (2 * 2\sqrt{3}) = (4\sqrt{3})$$ square feet

Kudos [?]: 402 [0], given: 645

The hexagon ABCDEF is regular. That means all its sides are the same l   [#permalink] 05 Nov 2017, 07:32
Display posts from previous: Sort by