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

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4 Answers

Duane Bryant Profile
Duane Bryant answered
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
Duane Bryant commented
PS: A and c are opposite sides and b and d are opposites sides.
Ray Dart
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
Ray Dart commented
And Oddman is the DB when it comes to obscure maths - very clever.
millicent williams Profile
millicent williams answered
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
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
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
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.
Oddman Profile
Oddman answered
If it is a trapezium, the side of length 75 is parallel to the side of length 15. The distance between them is about 19.7423 ft, so the area is about 888.403 ft^2. (The short diagonal can be computed from the Law of Cosines as (19√5)/2 ft.) If it is any other shape, additional information is needed.

The exact area of the trapezium is
  (3/8)√5612519 ft^2

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