# Area of plot four sides measured as 75 feet,70 feet,15 feet and 21 feet?

Is this a trapezoid (Br: Trapezium) where two bases are paralell? Is one side perpendicular to the paralell bases (= height)?  If both of these criteria are met, then the formula is: Area = [(base + base) x (height)]/2.  If neither side is perpendicular to the  paralell bases then the formula is: [(a+b)/(4(b-a))] x square root of: [(-a+b+c+d)(a-b+c+d)(a-b+c-d)(a-b-c+d)].  If this is just a quadrilateral with no paralell or perpendicular sides, you need Oddman to the rescue!
thanked the writer.
Duane Bryant commented
PS: A and c are opposite sides and b and d are opposites sides.
Ray Dart commented
We just need more information, I think. (Like an angle or two, or a statement that two sides are parallel).
Ray Dart commented
And Oddman is the DB when it comes to obscure maths - very clever.
We need a bit more information, do you have an angle or two to share with us?
thanked the writer.
Do we need angles Ray can't we just divide it into two triangles and do it that way,or am I missing something?
thanked the writer.
Ray Dart commented
My old poor brain.

If you imagine four thin strips of those lengths joined together with a hinge at each corner, would you not be able to move the whole thing around, making different plane figures, with resultant different internal areas?

Do we not need at least one angle to lock the whole thing into place?

I'm probably wrong - my brain is very old and has suffered many years of misuse.
Oddman commented
You are absolutely correct that more information is needed. Just saying the shape is a trapezium is sufficient additional information. An angle or a diagonal measure would also do it.
Oddman commented
I used to build figures from straws threaded together with string. Of course, a triangle will hold its shape, but a 4-sided figure will not. That is what we're talking about here. If there is no definite shape, there is no definite area.