Look At Me! Look At Me! Look At Me!

Calculus Level 3

Shirley is designing a float for an upcoming Parade. She has a 20 meter long wire, that she wants to use to form the outline of a square and/or an equilateral triangle.

To attract the most attention from the parade attendees, she wants to maximize the sum of areas of these shapes. To 1 decimal place, what is the maximum area that she can cover?

Image credit: Wikipedia
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