Roy, W7EL wrote:
'Ok, let`s start with a triangular loop with negligible loss."

"Negligible loss" eliminates the differences between loops of most
shapes with the same enclosed areas. Area of a triangle is 1/2 its base
times its altitude, if I remember.

I`d rather use 16 ft of wire to make a square loop with 4-ft sides. Side
squared makes an area of 16 sq ft.

A circle of 16 ft perimeter has a diameter of 6.09 ft. Radius is 3.049
ft. Squared, it`s 9,27. and times pi it`s 20.13 sq ft.

Clearly the circle has the greater area for the same wire. Loss is based
on the resistance of the wire which is the same in both cases.

For more enclosed area, you get more radiation for the same wire and
loss.

As a short cut, I`ll quote Terman on page 907 of his 1955 edition:
"The radiation resistance of a loop antenna is less the smaller the loop
area."

Best regards, Richard Harrison, KB5WZI