A lesson plan for deriving and applying the formula for the surface area of a pyramid.

Subjects:

Mathematics > General

Mathematics > Geometry

Education Levels:

Grade 9

Grade 10

Grade 11

Grade 12

Keywords:

geometry curriculum curricula three dimensional surface area pyramid

Language:

English

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Aim: How do we find the surface area of a pyramid?

Learning goals: Students will be able to determine the slant height of a pyramid. Students will be able to apply the formula SA = B + ½Pl to find the surface area of any pyramid.

Prerequisite knowledge: Students should be able to find the perimeter of a simple plane figure. Students should be able to apply the Pythagorean Theorem to find the hypotenuse of a right triangle.

Motivational problem: See diagram in "Other resources--Finding surface area of a pyramid"

Key ideas: B in the formula represents the base area. This is dependent on the shape of the base, which we will assume is a regular n-gon. The remainder of the formula is ½Pl. The area of each lateral face is ½bh where b is the base of the triangle and also one side of the regular polygon that is the base shape. The height of this lateral face is really the slant height so ½bh=½bl. Since there are n lateral faces, the area for all lateral faces is n(½bl). To find the base of one lateral face, b, we notice that it is 1?n(P) for the regular polygon with perimeter = P. So the surface area becomes n(½(1?n(Pl))) = ½Pl.

Important questions: How does your shape change if your base is not a regular polygon? Why doesn’t your formula change when the number of lateral faces changes?