Calculating Surface Area, and Volume of Right Pyramids.

If somebody asked you, whether or not you know the difference between a pentagonal pyramid, and a square pyramid; would you be able to give the right answer? Do you know the similarities, and differences between the height, and slant height? Do you know how the Pythagorean Theorem may help you in finding the surface area, and/or volume of a hexagonal pyramid, or any other one? Do you know how the formula for the surface area of a pyramid is related to the formula of a simple triangle?

You will be thrilled of visiting this lesson, and find out that those hard to answer questions are lay out in very simple terms with the use of your visual clues: Sequence of colors, and animations. We favor tapping at your visual side than giving you long explanations. After all your time is very valuable! In some problems you will have to work interacting with the lesson solving the specific problems by means of your stylus on the screen and the top section of the screen where the marker tools is located and pulled down by clicking on it.

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

Base of a conic solid
The planar region that forms the widest point of a conic solid; often labeled as the 'bottom' of the conic solid, it determines the exact shape of the conic solid.

Conic solid
The set of points between a point (the vertex) and a non-coplanar region (the base), including the point and the region.

A segment that helps to make up a face.

A polygonal region of a surface.

Lateral area.

Lateral area
The area of the lateral surface of a solid.

Lateral edge
A segment whose endpoints are corresponding points of a cylindrical solid's bases, or whose endpoints are the vertex of a conic solid and a vertex of its base.

Lateral faces
The faces of the lateral surface of a prism, or a face of a pyramid that is not a base.

Lateral surface
The surface not included in the base (s).

A three-dimensional surface which is the union of polygonal regions and has no holes.  

It is a polyhedron whose base is a polygon and whose lateral faces are triangles with a common vertex called the vertex of the pyramid. The perpendicular segment whose endpoints are at the base and at the vertex of the pyramid is the altitude, which is the height of the pyramid. A regular pyramid has congruent isosceles triangles in the lateral faces and a regular polygon in the base. The length of the height for the lateral triangles is the slant height for the pyramid.

Regular pyramid
A pyramid whose base is a regular polygon and whose vertex forms a segment with the center of the polygon perpendicular to its plane.

Slant height
The length of a lateral edge of a conic solid.

The union of the surface and the region of space enclosed by a 3-D figure; examples: conic solid, cylindrical solid, rectangular solid.

Solid geometry
The study of figures in three-dimensional space.

The set of all possible points; made up of infinite planes.

The boundary of a 3-D figure.

Surface area
The total area of the surface of a solid.

Unit cube
Unit of measuring volume.


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