# Math Help - Percentage area.

1. ## Percentage area.

OK the following question isn't really significant, but it should be relevant to understanding the problem:

In a study, team of researchers intends to use a square frame, 1 m^2 in area, 15 times within each of two 25 m^2 plots of land to study the number of species of plants in that area. Do you think that this is a sufficient number of replicates (repeat experiments) for this study? Give one reason for your answer.
As I said the question itself isn't significant, so it's not important if you understand what it's about, because all it's asking what percentage is are 15 sections of land 1 m^2 in area out of a total area of 25 m^2.

In a study of this nature, you are expected to study an area of at least 30% the size of the total area studied for your results to be considered significant. (That's 30% of each 25 m^2 area of land).

But here's the rub. I'm dumb, lol. I know it should be easy enough to calculate a simple percentage, but I'm a bit old and senile and I can't work out how to deal with this problem.

Firstly how many 1 meter squares are in 25 m^2? I know this is just 25 x 25 which = 625. So is this 625 1 metre squares in an area of 25 m^2?

If so it doesn't matter that you take 15 random 1 m squares from each 25 m^2 area, because you can gather these random squares up to an area of 15 m^2. So the question then becomes what percentage is 15 m^2 out of 25 m^2.

So to do this I simply did 15/25 x 100 = which = 60%. So in this case, as the answer is 60% (I think!) then the the 15 separate 1 metre squares are sufficient for this study.

Can anyone please confirm for me that my maths is correct?

2. ## Re: I must be dumb! Silly question about percentages?

squares with area of 25 m^2 have sides = 5 m ; c'est bon?

3. ## Re: I must be dumb! Silly question about percentages?

"Twenty five square meters" is NOT "twenty five meters square"!

The first means a region of the same area as a square 5 meters on a side, it could be of any shape. The second means specifically a square 25 m on a side. In any case, $15 m^2$ and $25 m^2$, because of the " $m^2$" units are both already areas. The ratio of areas is $\frac{15}{25}= \frac{3}{5}= 0.60$ or 60%.