Area of trapezoid, did I count right? Top and bottom lines are parallel. Trapezoid: ![trapezoid\]]( I got ~$6397 m^2$

Let's use:

$$A=\frac12(76\sin 72°)(100+77)=6397$$

Note that the result seems to be numerically exact 76*sin(72°)*177/2*177%2F2).

However note also that the left side should be $\geq 76 \sin 72°\approx72.28$ (maybe it's a typo?).

In case the bottom and top lines were not parallel you could consider a diagonal and solve for triangles or use Bretschneider's formula.

Notably, with reference to the following figure:

![enter image description here](

we obtain from the Law of cosines

$$AB^2=AC^2+BC^2-2AC\cdot BC \cos 72°\implies AB=115.9$$

and thus

$$S_{ABC}=\frac12AC\cdot BC \sin 72° = 3614$$

and from Heron's formula

$$S_{DBC}=\sqrt{p(p-a)(p-b)(p-c)} \approx 2710.65$$

and finally

$$S_{ABCD}\approx 6324.65$$