Brayden's Blog Post

For homework today everyone had to make a blog on 1 question. The question I recieved was..

A rectangular prism measures 16cm by 8cm by 5cm. It is cut so that the 16cm side is cut in half. How does the surface area of the half prism compare to the surface area of the original prism?

First I had to find the surface area of the original prism.

L = 16cm W = 8cm H = 5cm

S.A. = 2 (l x w) + 2 (l x h) + 2 (w x h)
S.A. = 2 (16 x 8) + 2 (16 x 5) + 2 (8 x 5)
S.A. = 2 (128) + 2 (80) + 2 (40)
S.A. = 256cm + 160cm +80cm
S.A. = 496cm2

Then I had to find the surface area of the half prism.

L = 8cm W = 8cm H = 5cm

S.A. = 2 (l x w) + 2 (l x h) + 2 (w x h)
S.A. = 2 (8 x 8) + 2 (8 x 5) + 2 (8 x 5)
S.A. = 2 (64) + 2 (40) + 2 (40)
S.A. = 128cm + 80cm + 80cm
S.A. = 288cm2

Now to compare.

You would think that cutting the prism would mean that the surface area is divided by 2, but, it isn't. It is not half because when you split it vertically the only dimension that changes is the length. So when you are multiplying width by height it will be the same as the original prism. When you look at the answer every thing is cut in half except the width by height. Therefore the surface area of the half prism is not half the surface area of the original prism.

Please correct me on my mistakes.

COMMENT!