platypus

You need a pencil, paper, measuring tape, calculator, and a penny.

Since the 8 sides of the room are all different lengths, no set of opposite sides will be parallel.
The above encompassing square solution would not be accurate.
However, it may be accurate enough for your purposes.

But, if you want to be exact...

Place penny on the floor in the approximate center of the room.
Drawing the layout as you go, measure the distance from the
penny to each corner of the room. You already know the lengths
of the side walls so this will give you the dimensions of 8 triangles.

Use Heron's formula to calculate the area of each triangle.

Given the sides of a triangle A,B,C first calculate the semi-perimeter S.

S = (A + B + C)/2

The area of the triangle is the square root of (S(S - A)(S - B)(S - C))

Now add together the areas of the 8 triangles. This gives you the area for the irregular octagon room.

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Out the 10Base-T, through the router, down the T1, over the leased line, off the bridge, past the firewall...nothing but Net.