Surface Area of Pyramids

Pyramid – A polyhedron with all faces except one intersecting a vertex. Pyramids are named for their bases, which can be a polygon of any variety.

Surface Area of Pyramids

Lateral Faces – The faces that intersect at the vertex. For a pyramid, they are all triangles.

Lateral Edges – The edges of the lateral faces that have the vertex as an endpoint.

Altitude – The segment from the vertex that is perpendicular to the base.

Surface Area of Pyramids

Axis – A line segment from the vertex of a pyramid to the center of its base.

Right Pyramid – A pyramid in which the altitude and the axis are the same segment. In this case, the base does not have to be a regular polygon.

Surface Area of PyramidsRegular pyramid – A

pyramid in which the altitude and the axis are the same segment and the base is a regular polygon. In a regular pyramid, each of the lateral faces is a congruent isosceles triangle.

Slant Height – The height of each lateral face of the pyramid. It is represented by l (lower case L).

Surface Area of Pyramids

Lateral Area of a Regular Pyramid

• If a regular pyramid has a lateral area of L square units, a slant height of l units, and its base has a perimeter of P units, then

L = (1/2)*P*l

CAMPING A pyramidal shaped tent is put up by two campers. The square base is 7 feet on a side and the slant height of the tent is 7.4 feet. Find the lateral area of the tent.

Answer: 103.6 ft2

Surface Area of Pyramids

Surface Area of a Regular Pyramid

• If a regular pyramid has a surface area of T square units, a slant height of l units, and its base has a perimeter of P units and an area of B square units, then

T = (1/2)*P*l + B

Find the surface area of the regular pyramid to the nearest tenth.

Answer: 89.8 m2

Find the surface area of the regular pyramid.

Answer: about 298.2 cm2