KJW said:

dv said:

KJW said:

The area is 18(cos²θ + sinθ cosθ)

The angles I chose to test the assumption were θ=45° and θ=0°, both leading to an area of 18, but it should be clear that the area isn’t 18 for other angles.

I get 18 for theta = 30 as well.

The base b of the rectangle would be 6 cos30 = 3 sqrt(3)
The height of the triangle would be 6 sin 30 = 3
Pythag:
r^2 = 3^2 + (b – r)^2
r^2 = 3^2 + (3 sqrt(3) – r)^2
r^2=- 9 + 27 -6 sqrt(3)r + r^2
r = 2 sqrt(3)

A = r b = 18

My formula above doesn’t give 18 for θ=30°. Note that cos30° ≠ sin30°.

Yeah I think your formula is wrong