How do one calculate the area (m^2) of freeform shapes?

Question

Ok, ill be honest, i'm building a patio, and for that i'd like to estimate the cost using sqm. However the shape of the patio is what you might call non-standard.

So far i've been able to use rectangles and triangles formulas to calculate sqm of the other areas of my garden. But not in this case.

My non standard shape, basically have the following measurements.

wx = width x
dx = depth x

w1 = 8.2m
w2 = 5.1m
d1 = 7.2m
d2 = 4.2m

Now, is it possible to calculate the area of this with the information that i provide? If so, how?

Would the following be a correct estimate?

(8.2*7.1)/2 + (5.1*4.2)/2 = 40.23

Any help on this is appreciated.

Answer 1

You can break it up into shapes you know how to calculate the area of, like rectangles, triangles, sectors of circles. If the shapes don't cover it completely, or stick a little beyond, the error may be small enough. If not make smaller pieces.

Another approach is to rule off parallel lines on meter centers-a chalk line will make that easy. Now rule off another set perpendicular to the first. Count the squares like graph paper. Estimate any partial squares. Again, you should be pretty close.

Answer 2

You have a quadrilateral $ABCD$. Its area cannot be determined from the side lengths of $AB$, $BC$, $CD$, $DA$ alone. You need further information such as the length of the diagonal $AC$ or $BD$, or one of the interior angles of the quadrilateral.

If you have that extra piece of informtation, you can segment the quadrilateral into two triangles and compute their areas then add the two areas.