The turbulent flame surface is typically highly wrinkled and folded at a multitude of scales controlled by various flame properties. It is useful if the information contained in this complex geometry can be projected onto a simpler regular geometry. This will also enable the use of spectral, wavelet or multifractal analysis. Here we investigate the local flame surface statistics of turbulent flame expanding under constant pressure. First the statistics of the local length ratio is experimentally obtained from highspeed planner Mie scattering images. For our spherically expanding flames, the length ratio on the measurement plane, at predefined equiangular sectors is defined as the ratio of the actual flame length to the length of a circular-arc of radius equal to the average radius of the flame. Assuming isotropic distribution of such flame segments we convolute suitable forms of the length-ratio probability distribution functions (pdfs) to arrive at the corresponding area-ratio pdfs. It is found that both the length ratio and area ratio pdfs are near log-normally distributed and show self-similar behavior with increasing radius. Near log-normality of the flame-length ratio suggests similarity with dissipation rate quantities.