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Q&A #19123


Surface Area of Prisms

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From: Jeanne (for Teacher2Teacher Service)
Date: Dec 03, 2007 at 23:46:26
Subject: Re: Surface Area of Prisms

Hi Harvey,

Let me begin by letting you know what I believe the letters in the formula, S
= Ph + 2B, stand for. S = surface area. B = area of a base of the prism. P
= perimeter of the base. h = height of the prism.

I've never taught this formula, but if I did, like Gail, I'd start by cutting
apart a box. But in order to help students see the two bases (2B), I would
use prisms that have bases that not rectangles or squares. Craft stores are
good places to look for such boxes. I've seen candy boxes that are triangular
and hexagonal prisms.

I'd make sure I have two identical boxes, one to cut apart and one for the
students and me to use as a reference.

Let's focus on a hexagonal based prism.

Cut out the two hexagon bases along the edges.  The area of these two
hexagons are 2B.

After you cut out the bases, you're left with a hexagonal tube.  To figure
out the area of the hexagonal tube, it is helpful to cut along ONE edge.  The
tube opens up to a big rectangle.  The height of the tube (h) is the height
of the big rectangle.  The perimeter of the tube (P) is the width of the big
rectangle.

Area of the big rectangle = base times height = width times height = Ph

So the total surface are of the prism equals the area of the big rectangle
plus the area of the 2 hexagon bases.

S = Ph + 2B

This was pretty rough, but I hope it gave  you some ideas.  Good luck.

 -Jeanne, for the T2T service

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