Requesting Calculation of Residential Plot area with 4 unequal Lenth

You will need an angle or a diagonal measurement. With only the lengths of the sides the area plot could be many different sizes.
If you assume it is nearly square then you could have an area of approx 11 x 16 Sq metres (176) but you can't get an accurate value from just that information given.

Thibault... is right.
Consider a rectangle.  IF you push the top side to the right far enough the area will approach zero.
Consider the estimate of the area given you. It is a good one and is about the largest area you can get from those measurements. It is 176 sq meters. If you estimate 3 feet to a meter the estimate is about 1600 sq feet. Much less than the desired 2160 sq feet. You need a larger housing plot.

I think the 2160 sqft was an estimate and the area is something less.  The only method I know that could be used to calculate the maximum area would be to draw a diagonal forming two triangles.  Then, write 2 semi-perimeter equations for each triangle forming a function and take the derivative and solve for the maximum area.  I started to do this but it got two involved.  I couldn't find anyway to put the sides together to come closer to 2160 sqft than 2133 sqft.

You would need the survey data to accurately determine the area.  The survey data would show the direction and length of each side.

Using trial-and-error with (2) semi-perimeter equations, I found an approximate maximum value of about 200 sq-meters that is less than 2160 sqft by about 200 sqft.  This approximate maximum was with a diagonal BD of about 20 meters.

I never thought of it before this question but I think any polygon inscribed in a circle with all vertices on the circle is the maximum area.  Seems reasonable since a circle encloses the maximum area for a given perimeter that a cyclic polygon would enclose the maximum area.

Thanks to d-glitch for taking the time to set up the spreadsheet.

I am very delighted to find a best solutions made by d-glitch. The Expert did a lot of calculations and applied Excel application to accomplish the assignment. I am happy with the Quadrilateral-Calculation-for-ExEx.xlsx and details of the deliberations.
Thanks expert of d-glitch for his untiring endeavor.
Best wishes,
Sikder

Just note that noone found the correct answer because there is not enough information.

The answer given is the maximum possible area.  To get your correct answer we need an angle or diagonal information.

The asker in ID: 41806096 essentially awarded d-glitch the points. In my mind Thibault... first pointed out the inadequacy of the data furnished so he should get a few points.

I agree with "aburr".  Even finding a maximum requires that you assume the quadrilateral is a cyclic quadrilateral.