[Math] Calculate pentagon area based on lengths of all its sides

areageometrypolygons

Sorry for this question. I guessed there is an online calculator to calculate the area of the pentagon if we know lengths of all its five sides. Actually there isn't

So, here are the lengths of sides of pentagon ABCDE:
AB=19.14;
BC=111.73;
CD=33.23;
DE=14.66;
EA=110.75;

Q1. What is the area of this pentagon?

Also, there are more questions:

Q2. what's the formula to calculate the area of the pentagon based on its side lengths (side order counts)?

Q3. How many pentagons are possible to build if we know the side lengths? (of course, side order counts!)

Q4. Is this statement truthful: You can build the pentagon based on its side lengths then and only then when the side length is smaller then the sum of other sides, and it is also valid for all (other) sides.

Thank you.

Best Answer

  1. You can't tell. You can change the angles, and then the area will change.

  2. From answer 1, there is no formula.

  3. An infinite number (uncountable).

  4. No.

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