Irregular objects can have their perimeters measured in a variety of different ways. Probably the easiest is to run a string along the edge of the object and then later lay the string flat and measure it. Another way is to measure in partial straight segments and approximate.
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If you wanted to describe the length and breadth of an irregular shape you would find the maximum length and breadth. You could sandwich the object between two flat boards, and measure the distance between the boards. Then rotate the object 90o and do it again, for the breadth.
If the object is irregular the best way is to measure the volume of water it displaces when you immerse it completely in water.
I would place it in a container full of liquid after measuring the liquid. I would measure the amount of liquid displaced by the object. That amount is equal to the volume of the irregular object if it is fully submerged in the liquid.
You need to measure the length of each line segment or arc and then sum them.
Use the water displacement method. The object is equal to the amount of water it displaces. :)