Converting "PERIMETER" to "AREA"

Question

If my perimeter is 755 square feet what is my area in square feet? My measurements are 198ft x 202ft x 145ft x 210ft.

Answer 1

Depending on the information given, different formulas can be used to figure the area of irregular quadrilaterals. Usually, the methods involve cutting the shape into two triangles, then finding the area of each triangle. The formula to find the area of each triangle will depend on the type of triangle involved.

If you have the lengths of each side (a,b,c,d) and the length of one diagonal (let's say the one going from the corner ab to the corner cd, call it e) then you can use Heron's formula twice to get the overall area:

Area = (SQRT(x(x-a)(x-d)(x-e))) + (SQRT(y(y-b)(y-c)(y-e)))

Where x=(a+d+e)/2 and y=(b+c+e)/2

Answer 2

A 4-sided figure is called a quadrilateral.

 

You may divide a quadrilateral into other areas (for example, rectangle and triangles) to determine the total area.

 

With 4 side lengths, the area may have a range of values.  Usually, one angle is also specified so that the shape is fixed and the area may be calculated (using trig and Bretschneider's formula to calculate the area).