A pyramid is a three dimensional shape made up of a base and triangular faces that meet up at the vertex, V, which is also called the apex of the pyramid.

### Surface area of a pyramid

The surface area is composed by two parts: the area of the base and the lateral area.

#### Area of the base

It depends on the shape, you have to use the correct formula if the base is composed by a triangle, square, ecc.

#### Lateral surface

Since the side faces are triangles and the formula for the area of a triangle is

All you need to do is multiply the area of the base by the slant lenght and divide by two

Inverse formulae:

### Volume of the pyramid

Inverse formulae:

#### Exercises

- A pyramid has slant lenght 10 cm long. The base is a square with a side of 7 cm. Calculate the total surface area. Solution
- A pyramid has a slant lenght 125 cm long. The lateral surface is 450 dm
^{2}. Calculate the perimeter of the base. Solution - A pyramid has a volume of 1840 cm
^{3}. The base is a square that has an area of 1.84 cm^{2}. Calculate the height of the pyramid. Solution - The base of a pyramid is a rhombus, that has an area of 37 cm
^{2}. Calculate the lateral surface area knowing that the total surface area is 140.5 cm^{2}. - The base of a pyramid is an isosceles triangle ABC with AB = 10 cm and the height CH = 12 cm. The height of the pyramid is 15 cm. Calculate the volume of the pyramid.