What is the general formula to calculate the area of a piece of land with four unequal sides?

Question

It has an area of 655 square meters and the sides are 15.69, 40.72, 16.76 and 40.00 all in meters. All four angles are also known.

Answer 1

Depends on the shape, but an integral will work. Take a double integral and you should be able to find it ( you have 4 points, two per integral).

Answer 2

I think you would have to make the quadrilateral into smaller triangles and then use heron's theorem (if you have all the sides of the triangle) to find the area of each triangle.  

Answer 3

You stated that the area is 655 sq m, so I'm not sure of your question??

Answer 4

Multiply the average length and average width to get the area.

15.69 & 16.76 average to 16.225

40.00 & 40.72 average to 40.36

16.225 * 40.36 = 654.8

Double integral?  d**n, you people make easy stuff difficult!

Answer 5

It could have many different areas without changing the side lengths, just changing the angles.  Imagine 4 sticks of unequal length attached to each other at the endpoints with hinges.  It would not be rigid, and by moving the sticks you could get many different areas.

In short, you need more information.  If you know one of the diagonals that would be enough.  If you know two adjacent angles that would be enough.  If one pair of opposite sides is parallel it would be a trapezoid, and its area would be determined if you also know the distance between the parallel sides.

Even if all 4 sides are equal say to 10 feet, it is not enough information to know the area.  It could be a square, with area 100 square feet, or a very flat rhombus with all sides 10 feet but area nearly zero.

Answer 6

Rule av kosines:

spesify the (x,y) position av all the points around the rim av wotever.

make list x1, x2,...xn, x1 (gotta kloes the shape so last spot=first spot

repeet for y

add up the terms...termi=x(i)*y(i+1)-x(i+1)*y(i) for i=1, n

n=number av sides

area=sum/2

warning...tu get rite area, the points must be in order around the rim.  

If yu go klokwise yu get positive number, kounterklokwise, get netative, so take the absolute value.

Thank bout the process & yu will see that yu kan start at NE point...will get same anser.

Yu kan simplifi the math a littel bi set koordinates so that 1 point is (0,0).  In other werds, that area is the same if yu muve it around.  Yu kan even rotate it if yu want.

rule good for n=3, 4, 5...infinity