Find the surface area of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm.

To solve for the surface area of the pyramid, we make use of the formula:

A = l w + l [sqrt ((w / 2) ^2 + h^2) ] + w [sqrt ((l / 2) ^2 + h^2))

where,

l and w are the base of the pyramid = 100 mm

h is the height of the pyramid = 75 mm

Substituting the given values into the equation:

A = 100 * 100 + 100 [sqrt ((100 / 2) ^2 + 75^2) ] + 100 [sqrt ((100 / 2) ^2 + 75^2))

A = 10,000 + 100 (sqrt 2575) + 100 (sqrt 2575)

A = 20,148.90 mm^2

Therefore the surface area of the pyramid is about 20,149 mm^2.