In HRTEM image determine the diameter d of the nanoparticle. Determine the surface of a single nanoparticle by the formula S = pi x d2. For surface area of nano particles multiply the surface S of one nanoparticle by the number of particles.
As HRTEM gives you a 2D picture. you can analyze the picture and approximate the shape (think about which 3D structure gives you such projection). Measure directly the geometric parameters of your projection and this allows you roughly estimate the surface area by and using simple mathematical equation for the surface, knowing for example the value of radius or semi-axes.