how to find area of pentagon when points are given?

Question

points are given (x,y) like this

Answer 1

Choose an arbitrary point in the middle of those points (any point inside the pentagon). Draw (or imagine) the lines of the pentagon and the lines connecting each vertex to the center. Thus, you've seperated your pentagon into 5 disjoint triangles whose area comprosises the whole pentagon. Thus, the area of the pentagon is simply the sum of the areas of these triangles.
To find the area of any of the triangles calculate the distance of each side. You'll only have to calculate 10 distances (instead of 15) for the three triangles, because they share sides. To calculate the distance (which you probably already know) use sqrt( (x1-x2)^2 + (y1-y2)^2).
Then, use Heron of Alexandria's formula (which can tell you the area of a triangle if you know all the side lengths):

Area=sqrt(s(s-a)(s-b)(s-c)),
where s=(a+b+c)/2 or perimeter/2

Add the areas of all the triangles, and you get the area of the pentagon. The great thing about this method is that it works for any polygon. Pick 5000 points, and then pick a point inside the enclosed figure and you can (with the help of a computer, probably) calculate the area.

Answer 2

very simple. a pentagon has 5 equal sides i.e all its sides are equal.
so using distance formula get the vertices of the pentagon and then calculate the area.