This Lesson (OVERVIEW of LESSONS on Surface Area of PYRAMIDS) was created by by ikleyn(52781)   : View Source, ShowAbout ikleyn:
OVERVIEW of LESSONS on Surface Area of PyramidsFor your convenience, this file contains
- the list of my lessons on surface area of pyramids in this site,
- the major formulas for calculating the surface area of pyramids, and
- the list of relevant solved problems.
Examples of pyramidsFigures 1a - 1e present the examples of pyramids.
Figure 1a. Rectangular pyramid
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Figure 1b. Rectangular pyramid
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Figure 1c. Triangular pyramid
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Figure 1d. Triangular pyramid
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Figure 1e. Hexagonal pyramid
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Major formulas for calculating the surface area of pyramids
1. The lateral surface area of a pyramid is  =  (  +  + . . . +  ),
where  are the base edge measures and  are the slant heights, i = 1, 2, . . . , n.
2. The lateral surface area of a regular pyramid is =  =  ,
where  is the base edge measure,  is the slant height and  is the perimeter of the base polygon.
3. The total surface area S of a pyramid is  =  ,
where is the lateral surface area of the pyramid and  is the pyramid base area.
My lessons on surface area of pyramids in this site - Surface area of pyramids
under the topic Area and surface area of the section Geometry, and
- Solved problems on surface area of pyramids
under the topic Geometry of the section Word problems.
Solved problems on surface area of pyramidsLesson Surface area of pyramids
- Find the lateral surface area of a regular pyramid with the square base if the height of the pyramid is of 12 cm and the measure of the base edge is of 10 cm.
- Find the surface area of a regular tetrahedron if all its edges are of 10 cm long.
- Find the lateral surface area of a regular hexagonal pyramid if its base edge is of 4 cm and the height of the pyramid is of 6 cm.
- Find the surface area of a combined solid body of a "diamond" shape which comprises of two regular tetrahedrons joined face
to face, if all their edges are of 4 cm long.
- Find the lateral surface area of a body obtained from the regular tetrahedron with the edge measures of 10 cm after cutting
off the part of the tetrahedron by the plane parallel to one of its faces in a way that the cutting plane bisects the three edges
of the original tetrahedron.
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Lesson Solved problems on surface area of pyramids
- Find the surface area of a triangular pyramid ABCD if its edges issued from the vertex A are of 8 cm, 6 cm and 6 cm long
and each of these three edges is perpendicular to the two others.
- Find the surface area of a rectangular pyramid ABCDE if its base ABCD is a square with the side measure of 6 cm and the
lateral edge AE is perpendicular to the base plane and has the measure of 8 cm.
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- Find the lateral surface area of a regular pyramid with the square base if the lateral edge of the pyramid has the same measure
of 10 cm as the the base edge has. Then find the total surface area of the pyramid. Also find the angle between the lateral
edge and the base of the pyramid.
- Find the lateral surface area of a regular hexagonal pyramid if the base edge has the measure of 4 cm and the height of the
pyramid is of 2 cm. Then find the total surface area of the pyramid. Also find the angle between the lateral face plane and
the base plane of the pyramid.
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- Find the surface area of a combined solid body of a "diamond" shape which comprises of two regular rectangular pyramids with
square bases joined base to base, if all their edges are of 4 cm.
- Find the lateral surface area of a body obtained from a regular rectangular pyramid with the edge measures of 10 cm for all
edges after cutting off the part of the pyramid by the plane parallel to the base in a way that the cutting plane bisects the
four lateral edges of the original pyramid.
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My lessons on surface area of pyramids and other 3D solid bodies in this site are
To navigate over all topics/lessons of the Online Geometry Textbook use this file/link GEOMETRY - YOUR ONLINE TEXTBOOK.
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