Math CentralQuandaries & Queries


Question from Robert, a parent:

I have a wall 40 ft. long and 4 ft. tall as well as another one that is 30 ft by 3.5 ft. tall that I am trying to build. how many 6 inch by 12 inch landscaping blocks do I need?

Hi Robert,

your first wall is 40 ft by 4 ft so its surface area is $40 \times 4 = 160$ square feet. Your second wall has a surface area of $30 \times 3.5 = 105$ square feet. Thus you have a total surface area of $160 + 105 = 265$ square feet. Each block is half a foot by one foot so its area is $\large \frac12 \normalsize \times 1 = \large \frac12$ a square foot. Hence you will need at least $265 \times 2 = 530$ blocks. I say at least since there is bound to be some wastage. In particular if you arrange the blocks in the typical pattern

block wall

Image from

then every other row will require cutting a block. Can you do so and save the half block you cut off or do you loose half a block at each end?


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