A square pyramid has side lengths of 10 units and a height of 7.6 units. The slant height of each lateral face is 9.1 units. What is the surface area of the pyramid to the nearest unit?

The answer is 282 square units.

The surface area (SA) of the sum of the area of its base (A1) and 4 areas (A2) of the slant side. It is 4 because it is the square pyramid and it has 4 slant sides.

SA = A1 + 4A2

The area of the base (A1) is the area of the square with side a:

A1 = a²

The area of the slant area (A2) is of the square pyramid with side a and slant height s is:

A2 = a · s / 2

So, it is known:

a = 10 u

s = 9.1 u

Therefore:

SA = A1 + 4A2 = a² + 4 · a · s / 2 = a² + 2 · a · s = 10² + 2 · 10 · 9.1 = 100 + 182 = 282 u²