Find the pyramid's base and count its sides. If the base has three sides, the pyramid consists of four triangles, one for its base and three for its faces. If the triangle's base has four or more sides, then the pyramid has that many triangular sides, or faces. For example, a triangle with a pentagonal base, a polygon with five sides, has five faces.
Multiply the base's perimeter by its slant height if the base is a regular polygon --- each side is identical in length --- to calculate the pyramid's lateral area, which is the total area of its faces. If the base is not a regular polygon, find the area of each of the triangular faces through the formula for triangular area --- ½ * altitude * base length, then sum those areas.
Calculate the base's area with the proper area formula of the base's shape, then add the area to the pyramid's lateral area to calculate the pyramid's total surface area.
Multiply the pyramid's base area by its height, then divide the product by three to calculate the pyramid's volume.