MHB Express rectangle area as function of x

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The area A of the rectangle can be expressed as A = x(36 - x^2), where x is the length along the x-axis and the height is determined by the graph y = 36 - x^2. The domain of A is 0 ≤ x ≤ 6, as the rectangle's corners must remain within the first quadrant. To find the maximum area, the function A can be analyzed using calculus, revealing that A is largest when x = 3. The maximum area occurs at this value, providing a clear solution to the problem.
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Hey so another expressing functions question:

A rectangle has on corner on the graph of y=36-x^2, another at the origin, a 3rd on the positive y-axis, and the fourth on the positive x-axis. Express the area A of the rectangle as a function of x. What is the domain of A? For what value of x is A largest?
 
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Let's look at a diagram:

View attachment 2132

In terms of $x$, what is the base of the rectangle...what is its height?
 

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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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