Surface Areas of Pyramids Find the lateral areas

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Surface Areas of Pyramids – Find the lateral areas of regular pyramids. – Find

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: • All of the

LATERAL AREAS OF REGULAR PYRAMIDS Pyramids have the following characteristics: • All of the faces, except the base, intersect at one point called the Vertex vertex. Lateral • The base is always a polygon. Edge • 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. Base • The altitude is the segment from the vertex perpendicular to the base. Lateral Face Altitude

LATERAL AREAS OF REGULAR PYRAMIDS Vertex Lateral Face Slant Height Lateral Edge Base Altitude

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

LATERAL AREAS OF REGULAR PYRAMIDS All of the faces of a regular pyramid are

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 the slant height l of the pyramid Slant Height Altitude l Base (a regular polygon) Regular Square Pyramid

LATERAL AREAS OF REGULAR PYRAMIDS The figure below is a regular hexagonal pyramid. The

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 s l s s s s l s s

LATERAL AREAS OF REGULAR PYRAMIDS l l s l s s s ½ l

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

Key Concept Lateral Area of a Regular Pyramid If a regular pyramid has a

Key Concept 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 = ½Pl l

Example 1 Use Lateral Area to Solve a Problem BIRDHOUSES The roof of a

Example 1 Use 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

SURFACE AREAS OF REGULAR PYRAMIDS The surface area of a regular pyramid is the

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.

Key Concept Surface Area of a Regular Pyramid If a regular pyramid has a

Key Concept 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 = ½Pl + B l

Example 2 Surface Area of a Square Pyramid l 24 18

Example 2 Surface Area of a Square Pyramid l 24 18

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

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