Hello, Aquameatwad!

I don't believe the problem is asking for the largest possible base.

A circle wih R=24 has a inscribed trapezoid with the largest ? base

twice as long as other base and the two sides.

Find the length of the sides of the trapezoid and its area?

I think it is referring to the *longer* base:

. . "The longer base is twice as long as the other base **and** the two sides."

Then the trapezoid looks like this:

Code:

24
* - - - - - *
/ . . \
/ . . \
24 / . . \ 24
/ . . \
/ . . \
* - - - - - * - - - - - *
24 24

The trapezoid is half of a regular hexagon.

It is comprised of three equilateral triangles with side 24.

You should be able to calculate its area.