CK-12 Geometry-Concepts

(Marvins-Underground-K-12) #1

http://www.ck12.org Chapter 11. Surface Area and Volume


When a pyramid has a height that is directly in the center of the base, the pyramid is said to beregular. These
pyramids have a regular polygon as the base. All regular pyramids also have aslant heightthat is the height of a
lateral face. Because of the nature of regular pyramids, all slant heights are congruent. A non-regular pyramid does
not have a slant height.


Surface Area


Using the slant height, which is usually labeledl, the area of each triangular face isA=^12 bl.


Surface Area of a Regular Pyramid:IfBis the area of the base andPis the perimeter of the base andlis the slant
height, thenSA=B+^12 Pl.


If you ever forget this formula, use the net. Each triangular face is congruent, plus the area of the base. This way,
you do not have to remember a formula, just a process, which is the same as finding the area of a prism.


Volume


Recall that the volume of a prism isBh, whereBis the area of the base. The volume of a pyramid is closely related
to the volume of a prism with the same sized base.Investigation: Finding the Volume of a Pyramid


Tools needed: pencil, paper, scissors, tape, ruler, dry rice or sand.



  1. Make an open net (omit one base) of a cube, with 2 inch sides.

  2. Cut out the net and tape up the sides to form an open cube.

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