Hi cd,
Something like this?

The image above is composed of three shape and a mask. The cyan shape is a rectangle with an aspect ratio of 2:1 (w:h).
The purple shape is a duplicate of the cyan shape. Both have been formatted from the 'square' shape in the shapes button menu to:
- set the stroke to None
- set the fill colours to the colours you want.
The two rectangles were then placed together, one above the other, with their edges abutting (a slight overlap is also acceptable), then Grouped using the Arrange menu item of that name.
Format (menu) > Mask with shape shows all shapes greyed when accessed with an inserted shape selected, so the next step was to take a screen shot (to the clipboard) of the two coloured square, then paste that screen shot back into the Pages document, thus changing it from a group of two inserted shapes to a png image of that shape.
Select the pasted image and go Format > Mask with Shape > Oval. Edit the mask to the size you need to fit the full width or height of the 'square' (which will now probably be a 'not quite square').
With the circle now defined, add a Square shape, and resize it to cover the circle with as much overlap as you need.
Select the square, and move it toward the back until it is behind the circle.
Select both the circle and the square, the go Arrange > Align > Center, then Arrange > Align > Middle.
Make any additional adjustments to the size and shape of the square, and repeat the Arrange steps. What satisfied, select both shapes, then go Arrange > Group to combine them into a single object which you can then resize to fit your need.
Regards,
Barry