What is the square feet of a lot with dimensions 117x60x108x75?

Answer 1

Draw it out to scale on squared graph paper, then count the small squares. Start with a base line of 117, then draw arcs based on each end of this line, of radius 60 and 75. Then find a line connecting the two arcs which is 108 long. That defines the shape, which is obviously not a standard one. It is possible to find a "maximum area" for the given dimensions, but if the length of the sides is the only thing you know, you're guessing or estimating.

It is not possible to solve for the area of an irregular quadrilateral if you know all the side lengths and nothing else. Visualize a simple square or rectangle made of sticks. The corners are attached in a way that the sticks can move. The shape can be "squished" and "stretched" to change its shape - and its area. And all of this can be done without the sides changing dimension. You can see where just having only the side lengths won't be sufficient to solve for the area of a lot in the shape of an irregular quadrilateral.

Irregular shapes, particularly ones bounded by straight edges, will all "break down" into triangles, and you will be able to solve them applying the principles of trigonometry. For any irregular 4-sided shape, draw a diagonal across it from one vertex to another (it doesn't matter which ones you use), and then draw perpendiculars from the remaining two vertices to the diagonal you drew to begin with. These two verticals will the the height of the two original triangles, and by measuring the length of the diagonal and those two heights, you'll have the base and the heights of the two original triangles. You'll then do the "1/2 bh" thing (one half the base times the height) to find the area of each triangle. Add the area of each triangle and you're done.

If you have two or even just one right angle in your lot, you're off to the races and you can solve it without taking any other measurements. Actually, if you have the measure of just oneangle, right angle or otherwise, you can hammer this and find an by using the power of trigonometry. With the angle you have and the two side lengths that form that angle, you have a triangle that is easily quantified. You can find the length of the third side and the area of that triangle. And by taking the length of the third side of that triangle you just worked with, know what? It's the length of the third side of the other triangle, and you have the dimensions of that triangle and can calculate its area. Add the two areas and you're done.