  We derive an approximate but fully explicit formula for the mean
first-passage time (MFPT) to a small absorbing target of arbitrary shape in a
general elongated domain in the plane. Our approximation combines conformal
mapping, boundary homogenisation, and Fick-Jacobs equation to express the MFPT
in terms of diffusivity and geometric parameters. A systematic comparison with
a numerical solution of the original problem validates its accuracy when the
starting point is not too close to the target. This is a practical tool for a
rapid estimation of the MFPT for various applications in chemical physics and
biology.
