Math CentralQuandaries & Queries


Question from Steven, a student:

I have been given a coursework in which i have to investigate various shapes to find the one that would give the largest area with 1000m perimeter. I'm stuck in a part where i have to calculate the area of a irregular pentagon. i don't know where to start from. I can make up the length of all the sides (5 sides), so long they add up to 1000, but i'm not quite sure what to do after that.
Please i require your help.
Thanks for your time.

Hi Steven,

Since this is an investigation I think you can decide on the shape of the irregular pentagon, as long as the perimeter is 1000 metres. I would use a shape that makes finding the area easy, like perhaps a house.



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