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Surface Areas of Pyramids

Surface Areas of Pyramids. Find the lateral areas of regular pyramids. Find surface areas of regular pyramids. Pyramid at the entrance to the Louvre, Paris. LATERAL AREAS OF REGULAR PYRAMIDS. Pyramids have the following characteristics:

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Surface Areas of Pyramids

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  1. Surface Areas of Pyramids • Find the lateral areas of regular pyramids. • Find surface areas of regular pyramids. Pyramid at the entrance to the Louvre, Paris.

  2. LATERAL AREAS OF REGULAR PYRAMIDS • Pyramids have the following characteristics: • All of the faces, except the base, intersect at one point called the vertex. • The base is always a polygon. • The faces that intersect the vertex are called lateral faces and form triangles. The edges of the lateral faces that have the vertex as an endpoint are called lateral edges. • The altitude is the segment from the vertex perpendicular to the base. Lateral Face Vertex Lateral Edge Altitude Base

  3. LATERAL AREAS OF REGULAR PYRAMIDS Lateral Face Vertex Slant Height Altitude Lateral Edge Altitude Base(a regular polygon) Base Square Pyramid Regular Square Pyramid

  4. LATERAL AREAS OF REGULAR PYRAMIDS All of the faces of a regular pyramid are congruent isosceles triangles. The height of each lateral face is called theslant height lof the pyramid Slant Height Altitude l Base(a regular polygon) Regular Square Pyramid

  5. LATERAL AREAS OF REGULAR PYRAMIDS The figure below is a regular hexagonal pyramid. The lateral area L can be found by adding the areas of all of its congruent triangular faces as shown in the net. l l l l l l s s s s s s l s s s s s s

  6. LATERAL AREAS OF REGULAR PYRAMIDS l l l l l l s s s s s s l s s s s s s ½ L = ½sl + ½sl + ½sl + ½sl + ½sl + ½sl = ½l (s + s + s + s + s + s) = ½Pl

  7. Key ConceptLateral 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 = ½Pl l

  8. Example 1Use Lateral Area to Solve a Problem BIRDHOUSES The roof of a birdhouse is a regular hexagonal pyramid. The base of the pyramid has sides of 4 inches, and the slant height of the roof is 12 inches. If the roof is made of copper, find the amount of copper used for the roof. L = ½Pl = ½(24)(12) = 144 12 4

  9. SURFACE AREAS OF REGULAR PYRAMIDS The surface area of a regular pyramid is the sum of the lateral area and the area of the base.

  10. Key ConceptSurface 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 = ½Pl + B l

  11. Example 2Surface Area of a Square Pyramid 24 l 18

  12. Example 2Surface Area of a Pentagonal Pyramid 17 in. 15 in.

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