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The figure above shows the lengths of the sides of an equian [#permalink]
Expert's post 00:00

Question Stats: 63% (01:27) correct 36% (02:41) wrong based on 41 sessions
Attachment: #GREpracticequestion The figure above shows the lengths.jpg [ 8.04 KiB | Viewed 1365 times ]

The figure above shows the lengths of the sides of an equiangular polygon. What is the area of the polygon?

(A) $$7$$

(B) $$8$$

(C) $$9$$

(D) $$\frac{14}{2}$$

(E) It cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The figure above shows the lengths of the sides of an equian [#permalink] We have a total of 5 small squares with side of 1 and 4 small right isosceles triangle with diagonal of 2^(1/2) or side of 1
--> Area = 5*1*1 + 4*1/2*1*1 = 7
--> A VP Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: The figure above shows the lengths of the sides of an equian [#permalink]
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Carcass wrote:
Attachment:
The attachment polygon.jpg is no longer available

The figure above shows the lengths of the sides of an equiangular polygon. What is the area of the polygon?

(A) $$7$$

(B) $$8$$

(C) $$9$$

(D) $$\frac{14}{2}$$

(E) It cannot be determined from the information given.

Here,

Let us assume the polygon to be a square, with 4 △'s as in the diagram attached

So the area of the polygon = Area of the square - 4 * Area of the △

Now let us take any one △,

We can see the hypotenuse = $$\sqrt2$$and it is a 45 - 45 - 90 triangle

Therefore each side is of equal length = 1

Now the area of the △ = $$\frac{1}{2} * 1 * 1 = \frac{1}{2}$$

Area of the square = $$side^2 = 3^2 = 9$$

Therefore the area of the polygon = Area of the square - 4 * Area of the △ = $$9 - (4 * \frac{1}{2}) = 7$$
Attachments FIG 1.jpg [ 7 KiB | Viewed 1629 times ]

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Manager Joined: 01 Jan 2020
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Schools: Copenhagen Business School - Class of 2022
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Re: The figure above shows the lengths of the sides of an equian [#permalink]
Basically just imagine that you have small squares and half squares and you are good to go

The numbers in the green are the areas of the shapes.
Attachments Image 06-05-2020 at 21.22.jpg [ 13.22 KiB | Viewed 626 times ] Re: The figure above shows the lengths of the sides of an equian   [#permalink] 06 May 2020, 11:25
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