Carpet is sold in square yards. How much carpet would a person need to buy for a rectangular room that has dimensions of 10 yard
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The area of a polygon = n*side^2 / (4 * tan(180/n))
where "n" is the number of sides
Let's calculate area for side = 2
area = 8*2^2 / (4 * tan(180/8))
area = 32 / (4 * tan(22.5))
area = 32 / 4*0.41421
<span> <span> <span> area = 19.3138746047 </span> </span> </span>
Now, let's calculate area for side = 6
area = 8*6^2 / (4 * tan(180/8))
area = 288 / <span> <span> <span> 1.65684 </span> </span> </span>
area = <span> <span> <span> 173.824871442 </span> </span> </span>
<span> <span> 173.824871442 </span> / </span><span><span>19.3138746047 = </span> 9
So, the area would be 9 times larger.
ALSO, looking at the formula
</span>n*side^2 / (4 * tan(180/n))
we can see that the side length appears just once in the formula and we are to square it in the calculation. So, if we increase the side length is increased by 3, then the area increases by 3^2 or 9.
where "n" is the number of sides
Let's calculate area for side = 2
area = 8*2^2 / (4 * tan(180/8))
area = 32 / (4 * tan(22.5))
area = 32 / 4*0.41421
<span> <span> <span> area = 19.3138746047 </span> </span> </span>
Now, let's calculate area for side = 6
area = 8*6^2 / (4 * tan(180/8))
area = 288 / <span> <span> <span> 1.65684 </span> </span> </span>
area = <span> <span> <span> 173.824871442 </span> </span> </span>
<span> <span> 173.824871442 </span> / </span><span><span>19.3138746047 = </span> 9
So, the area would be 9 times larger.
ALSO, looking at the formula
</span>n*side^2 / (4 * tan(180/n))
we can see that the side length appears just once in the formula and we are to square it in the calculation. So, if we increase the side length is increased by 3, then the area increases by 3^2 or 9.