How To Find The Area Of Irregular Pentagon?

By finding the area of irregular pentagon
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If you know how to find the determinant of a matrix, you can find the angle of ANY polygon, regardless of number of sides, angles, concave etc by the formula at

mathworld.wolfram.com you must have the coordinates of each point.  Otherwise, one of the methods listed by Iegoddard would be easiest.
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By definition, all sides of a regular polygon are equal in length. If you know the length of one of the sides, the area is given by the formula:

Area = (s^2) N /4 tan(π/N)

where:
S is the length of any side
N is the number of sides
π is PI, approximately 3.142
tan is the tangent function calculated in radians

in the case of a pentagon:
N = 5; tan(π/N) = tan(3.142/5) = 0.727
thus:
Area = (s^2) (5) / (4)(0.727) = 1.72 s^2
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Unlike a regular polygon, there is no easy formula for the area of an irregular polygon.  Each side could be a different length, and each interior angle could be different. It could also be either convex or concave.    So how to do it?  One approach is to break the shape up into pieces that you can solve - usually triangles, since there are many ways to calculate the area of triangles. Exactly how you do it depends on what you are given to start. Since this is highly variable there is no easy rule for how to do it. The examples below give you some basic approaches to try.    1. Break into triangles, then add In the figure on the right, the polygon can be broken up into triangles by drawing all the diagonals from one of the vertices. If you know enough sides and angles to find the area of each, then you can simply add them up to find the total. Do not be afraid to draw extra lines anywhere if they will help find shapes you can solve. Here, the irregular pentagon is divided in to 4 triangles by the addition of the red lines. ( See Area of a Triangle)    2. Find 'missing' triangles, then subtract the figure on the left, the overall shape is a regular hexagon, but there is a triangular piece missing.  We know how to find the area of a regular polygon so we just subtract the area of the 'missing' triangle created by drawing the red line. (See Area of a Regular Polygon and  Area of a Triangle.)    3. Consider other shapes In the figure on the right, the shape is an irregular hexagon, but it has a symmetry that lets us break it into two parallelograms by drawing the red dotted line. (assuming of course that the lines that look parallel really are!) We know how to find the area of a parallelogram so we just find the area of each one and add them together. (See Area of a Parallelogram). As you can see, there an infinite number of ways to break down the shape into pieces that are easier to manage.      You then add or subtract the areas of the pieces.   Exactly how you do it comes down to personal preference and what you are given to start.   ******Sorry the pictures didnt load look at www.mathopenref.com  Hope this helps =)
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Anonymous commented
But ho do i know what to cut the pentagon into like what kind of triangles?
A hexagon can be divided into how many triangles by drawing all of the diagonals from one vertex?
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I can just help you out and will tell you how to do it.

1-First take an example.

2-Divide the irregular pentagon in right triangles and rectangles.

3- Then find the area of each triangles and rectangle.

The are of the irregular pentagon will be the total sum of the area of all the triangles and rectangles.

Now try it and good luck with that!
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