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Q&A #19123 |
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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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