how can we obtain the areas of the irregular polygans or irregular shapes or just any closed curve...?? if we know the perimeter of that shape than do v need to divide it into any kind of simpler shape like triangle
eventually it all comes down to triangles (and maybe rectangles for parts of it)
To obtain the area of an irregular polygon or shape, you can use various methods depending on the information available.
If the shape is composed of straight sides and you know the lengths of those sides, you can use a method called triangulation. Triangulation involves dividing the shape into triangles and then finding the area of each triangle. The sum of the areas of the triangles will give you the area of the entire shape.
Here's how you can do it:
1. Divide the irregular shape into triangles: Draw straight lines inside the shape to divide it into smaller triangles. You can choose any points inside the shape and connect them to form triangles. It's important that all the triangles you form are non-overlapping and collectively cover the entire shape.
2. Calculate the area of each triangle: Once you have the triangles, apply the formula for calculating the area of a triangle, which is half the base multiplied by the height. Measure the base and height of each triangle using the given lengths or by using trigonometry if needed. Then, calculate the area of each triangle.
3. Sum up the areas: Add together the areas of all the triangles you calculated in the previous step. This will give you the area of the irregular shape.
By using triangulation, you can approximate the area of any irregular polygon or shape as long as you have the lengths of its sides.
It's important to note that this method may not provide a completely accurate result for highly complex shapes with curved sides. In such cases, more advanced mathematical techniques or computer-based algorithms may be necessary to accurately compute the area.