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I'm going to get possession of government plot of a housing plot. The total area should be 2160 sq feet equivalent to 3 (three) Katha (a local unit of measurement). The survey drawn a free hand sketch showing 4 length in meters like under

AB = 11.76 meter

BC=15.54 meter

CD = 10.24 meter

DA = 17,76 meter

No angle is marked in the sketch. Now what will be area in square feet or square meter of the plot. I urge those individual expert and expert group to exchange the calculation and help me to produce an area of the aforesaid plot.

Thanks and regards,

Sikder

AB = 11.76 meter

BC=15.54 meter

CD = 10.24 meter

DA = 17,76 meter

No angle is marked in the sketch. Now what will be area in square feet or square meter of the plot. I urge those individual expert and expert group to exchange the calculation and help me to produce an area of the aforesaid plot.

Thanks and regards,

Sikder

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.

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.

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.

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

Thanks expert of d-glitch for his untiring endeavor.

Best wishes,

Sikder

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

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182.03 sq meters ==> 1959.35 sq ft as dshindy has pointed out.

I have set point A at the origin (0, 0), and the longest segment (AD) as the base.

The coordinates of B (and the height of triangle ABD) are found by trigonometry.

The length of the diagonal BD is from the distance formula.

The area of triangle BCD is found from Heron's formula.

I could stop here, except that I want to make a plot.

Angle ABD is found from the Law of Sines.

Angle BDC is found from the area of the triangle and trig.

Finally the coordinates of C are found from the sum of the angles at D.

Quadrilateral-Calculation-for-ExEx.xlsx