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

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 △ = \(9 - (4 * \frac{1}{2}) = 7\)

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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.