Write the equation for the surface area of the triangular pyramid lattice shown in the image. Remember,
SA=(1/2base⋅height)+(1/2perimeter⋅inclined height)
The base is a triangle with h=14.72mm and its three faces are 17 mm
Around it there are 3 triangles with a base = 17 mm, its two faces each have 11mm and a height of 10.99mm.
SA = (1/2 * 17 * 14.72) + (1/2 * 3 * (17 + 2*11) * 10.99)
SA = (8.5 * 14.72) + (1.5 * 38 * 10.99)
SA = 125.12 + 584.55
SA = 709.67 mm^2
Therefore, the surface area of the triangular pyramid lattice is 709.67 mm^2.