Pyramids – The Triangular Mystery

By Mr. Martin

Pyramid

Pyramid: A polyhedron with only one base (can be any shape) and the lateral faces are all triangles that meet at a common vertex.

Altitude: The perpendicular segment from the vertex to the base (height is the length of the altitude)

Slant Height: The length of the altitude on a lateral face of the pyramid (denoted with an l)

Calculating LA and SA of regular pyramid

P = Perimeter of the baseL = Slant Height

B = Area of the Base

Example Numero Uno

P = 4 * 3P = 12

L = 2.5

LA = (1/2) * 12 * 2.5LA = 15

Example Numero Uno

LA = 15

B = ?? B = L * W

B = 3*3 = 9

SA = LA + B (15) + 9

SA = 24

Example Numero Due

P = 7 * 6P = 42

L = 13.4

LA = (1/2) * 42 * 13.4LA = 281.4

LA = 281.4

B = ?? B = (1/2)ap

B = (1/2)(6.1)(42)B = 128.1

SA = LA + B (281.4) + 128.1

SA = 409.5

Letter Go! Letter Go!Can’t find the slant height anymore!

To solve for LA of pyramids…all you need are 2 letters…

P

L

If you don’t have the slant height…but you have the altitude…you can use the Pythagorean Theorem!

Whaa???? We know the altitude but not the slant height…..

Find the Slant Height…..

Slant Height yo!

Now…find the surface area!!

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