Answer
$A=2h\sqrt{100-h^2}$ with $0\lt h\lt 10$
Work Step by Step
Let the base of the rectangle have length $b$.
We use the Pythagorean Theorem because half the base, the height, and the radius of the circle form a right triangle with the radius as the hypotenuse. Thus, we have:
$h^2+(b/2)^2=10^2$,
We solve for $b$:
$b=2\sqrt{100-h^2}$.
Then the area is the product of the base and the height of the rectangle:
$A=h\cdot b=h2\sqrt{100-h^2}$
with $0\lt h\lt 10$
