What is the area and perimeter of a square whose diagnol has a length of 10 square root of 2?

Answer 1

To answer this you've got to see that a square can be told as two equal triangles joined, right?

Ok, so, next, you use known ways to calculate remaining sides/angles/both of a triangle (for instance, if there are two angles with 30º each, the remainig will be 120º , so it gets a total of 180º, but that is not the exact purpose of this question, only of a step of it, so I won't go too far with it):

So, each of the two triangles that form a square would have two angles of 45º each (forming one of 90º joined with the other triangle's).

Then, if 1 side (lets say, side "c") has sqrt(10) of length, then each (lets say) "a" and "b" (remaining ones of the triangle) would have a lenght of about 2.236067977498.

So, what do we know now?

We know that each smaller side of the triangle has 2.236067977498, and that will correspond to the length of each of the square' s sides. So, for the perimeter:

2.236067977498x4=8.944271909992

For the area:

2.236067977498x2.236067977498=4.999999999991996234340004