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```6.3 Surface Area of Pyramids and Cones
OBJECTIVE: Determine the surface areas and lateral areas of pyramids and cones.
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6.3 Surface Area of Pyramids and Cones
The vertex of a pyramid is the point opposite the base of the pyramid. The base of a regular pyramid is a regular polygon, and the lateral faces are congruent isosceles triangles. The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base.
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The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid.
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B = area of base
h = height of prism P = perimeter of base
Surface Area
S=
L =
S = L + 2B
L = Ph
S = Ph + 2B
S
L = ½Pl
cube
= 6s
2
V = Bh
V rect prism = lwh
V cube = s3
S = L + B
S = ½Pl + B
L = 2πrh
S = L + 2πr2
S = 2πrh + 2πr2
V = Bh
V = πr2h
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Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and slant height 25 cm. Round to the nearest tenth, if necessary.
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Find the lateral area and surface area of the pyramid.
HINT:Use the Pythagorean Theorem to find ℓ.
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Find the surface area of the composite figure.
Surface Area of Cube without the top side:
Surface Area of Pyramid without base:
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HOMEWORK:
# 82 Pyramid Worksheet
L & S
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