Question

What is the formula to find out the area of an irregular pentagon?

Answer 1

Hint: We are given a question asking to find a formula to find the area of an irregular pentagon. First of all, we have a pentagon which is not a rigid polygon and so find the area indirectly by dissecting the pentagon into triangles of related shapes. But in the case of an irregular pentagon where sides are all different we cannot possibly have any formula to find the area unlike the case of a regular pentagon. Hence, there is no formula to find the area of an irregular pentagon.

Complete step by step solution:
According to the given question, we are asked to find the formula of the area of an irregular pentagon.
We know that a regular pentagon has five sides and each of the interior angles is equal to \[{{108}^{\circ }}\]. But the pentagon is not a rigid polygon and so we do not have the direct formula to find the area, we will have to dissect the pentagon into triangles of related shapes.
But in the case of an irregular pentagon, when all the sides are different (taking the maximum odds for an irregular pentagon). We cannot find the area of this given irregular pentagon directly, that is, we do not have the formula of area for an irregular pentagon.
Therefore, we do not have the formula to find the area of an irregular pentagon.

Note: We have stated in the above solution that the formula of area of an irregular pentagon cannot be found. But we can find the area of an irregular pentagon through indirect means. We can inscribe a circle. When we inscribe a circle touching maximum sides, we will have a radius of the circle, whose area we can find easily. Along with the circle, we will also get triangles as well. We will then have to find the area of those triangles. Then, the total area of the circle and the triangles will give us the area of the pentagon.