TITLE: How can I find the perimeter of a concave pentagon?
QUESTION [9 upvotes]: We know that a regular pentagon has five sides with identical lengths. But, the irregular pentagon has five sides with different angles. and moreover, the perimeter of a regular pentagon is 5a, where a is the side length of the regular pentagon. But how can I find out the formula of perimeter of an irregular concave pentagon? There is given a figure of a concave pentagon.

Here in the picture, the length of the AB and CD are Equal and the length of AB and BC are given. I have to find out the perimeter of the concave pentagon. I couldn't able to solve this anyway.

REPLY [2 votes]: The perimeter formula is 5a. Since it's a square with an inscribed equilateral triangle, the other two (triangle) sides are equal to the 3rd -- and the remaining 3 sides of the square.
3 sides of a square + 2 of a triangle