Geometry, 12.1: Surface area of prisms
Solid shapes with flat faces are called
The surfaces are called
and each is a
The lines where the faces intersect are called
Prisms have:
• 2 congruent, parallel faces called bases.
• parallel edges that connect corresponding vertices of the 2 parallel faces called lateral
edges.
• The faces that are not bases are called lateral faces.
Naming prisms:
• Named by the shape of the bases.
• Right if lateral edges are perpendicular to bases, oblique if not perpendicular.
Lateral Surface Area – the sum of the areas of the lateral faces.
Total Surface Area – the sum of the areas of the lateral faces plus the areas of the 2 bases.
Example: l = 14, a = 6, b = 8, c = 10
(a) Name the prism.
(b) Find lateral surface area.
(c) Find total surface area.
(d) How many lateral edges?
(e) How many lateral faces?
Practice:
(a) Name the prism.
(b) Find lateral surface area.
(c) Find total surface area.
Practice: l = 18, w = 9, h = 9
(a) Name the prism.
(b) Find lateral surface area.
(c) Find total surface area.
Practice:
(a) Name the prism.
(b) Find lateral surface area.
(c) Find total surface area.
Geometry, 12.2: Surface area of pyramids
Solid shapes with 2 congruent bases are called prisms
Solid shapes with only 1 base are called
Pyramids have:
• 1 base.
• Lateral edges which meet at a point called
the
A pyramid is a regular pyramid if:
• The base is a regular polygon.
• The lateral edges are congruent.
Therefore, the lateral faces of a regular pyramid are
isosceles triangles.
A quick review...
Identify the slant height and altitude:
Identify the lateral edge and altitude:
What kinds of triangles are determined from the sides above?
Example: Find the lateral area and the total area of the regular
pyramid:
Practice: For the regular, square pyramid:
(a) Find the area of each lateral face.
(b) Find the pyramid's lateral area.
(c) Find the pyramids total area.
Practice: For the regular, triangular pyramid:
(a) Find the area of each lateral face.
(b) Find the area of the base.
(c) Find the total area.
Practice: HW #7. A regular pyramid has a slant height of 12 and lateral edge of 15.
What is...
(a)...the perimeter of the base?
(b)...the pyramid's lateral area?
(c)...the area of the base?
(d)...the pyramid's total area?
Geometry, 12.3: Surface area of circular solids
3 solids that include circles:
Lateral Area:
L. A.cylinder = C ⋅ h = 2π rh
1
L. A.cone = C ⋅ l = π rl
2
none
(no lateral edges)
T . A.cylinder = L. A. + 2 Abase
Total Area:
= 2π rh + 2 (π r
2
)
T . A.cone = L. A. + Abase
= π rl + π r
2
Examples/Practice: Find the lateral area and the total area.
Find total surface area:
T . A.sphere = 4π r 2
Geometry, 12.4: Volumes of Prisms and Cylinders
What is volume?
Area = space inside a 2-D shape.
Volume = space inside a 3-D shape.
Volume of a rectangular box:
Vrect .box = lwh
Vrect .box = Bh
Try these...Find the volume.
Rectangular box with dimensions of 2in x 3in x 5in
Volume of other prisms:
V prism = Bh
Try these...
Find the volume of the triangular prism:
Volume of a cylinder:
Vcylinder = π r 2 h
Try these:
Find the volume of cement needed to form the concrete pedestal shown: