Question

What is the surface area of the regular pyramid below?1212A. 648 sq. unitsB. 396 sq. unitsC. 552 sq. unitsD. 522 sq. units

Answer 1

We can divide the surface of the pyramid into the following shapes:

and

In order to determine the surface area, we have to add the areas of all this shapes. That is, the area of 4 triangles and a square.

The area of a triangle is given by

`A_T=(b\cdot h)/(2)`

where b is the lenght of the base and h is the lenght of its height.

The area of a square is given by

`A_S=l^2`

where l is the lenght of its side.

So, in order to determine the surface area of the pyramid, we need to get:

`A_P=4\cdot(b\cdot h)/(2)+b^2=2\cdot b\cdot h+b^2`

since the sides of the squares are the bases of the triangles.

Using the data we have:

`A_P=2\cdot12\cdot21+12^2=504+144=648`

Thus, the surface area of the pyramid is 648 square units.