Question

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?

Answer 1

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