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Surface area of pyramids

A pyramid is a solid all of whose faces, apart from the base, are triangular and meet at a point. The type of pyramid is determined by teh base. If the base is a rectangle, we say the pyramid is a rectangular pyramid. If the base is a square its is a square pyramid and so on. To find the total surface area of a pyramid, first find the area of the base and then find the area of each triangular faces. The total surface area of the pyramid includes the area of the base and the area of all the triangular faces that make up the sides.

What is the surface area of this rectangular pyramid? Remember that a rectangular pyramid has 1 rectangular face and 4 triangular faces.

Find the area of each face. Add the areas of the 5 faces to find the surface area.

 Surface area
=
40 +
40 +
40 +
 40 + 64

= 224

The surface area of the rectangular pyramid is 224 square inches. What is the surface area of this rectangular pyramid when a=4, and h=12?