The way to find the lateral area of a square pyramid is by multiplying half the perimeter by the slant height. The method for calculating lateral areas of pyramids differs from the methods used to find lateral areas of prisms, cylinders and cones as pyramids have triangular faces with factors of one-half each.
In pyramids, the lateral area equates to half of the slant height multiplied by the perimeter. Slant height varies in value depending on the type of pyramid. Regardless of pyramid type, however, slant height is defined as the distance from the vertex of the pyramid to the base. This halfway point marks the center of the triangle, and is the middle distance between the vertices of the bases. The formula for determining the lateral area of pyramids works for most pyramids, with the exception of objects that have irregular shapes and oblique cones. Lateral area is more difficult to find in these types of pyramids, and often requires using calculus rather than geometry to solve. Once the lateral area is determined, the total surface area can be calculated. Surface area is the lateral area added to the area of each base, or twice the base area.