Carcass wrote:

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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 165 times ]

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