The area of a certain square is 64. What would be the area of second square whose perimeter was half as large as that of the first?

The area of any given square can be found by squaring the side length of that square. If s is a square's side length, then a = s². The perimeter of a square can be found by multiplying that side length by 4, since squares have four equal sides - mathematically, p = 4s. Notice what happens then when we cut the perimeter in half:

p/2 = 4s/2

We can either interpret this as only measuring half (2) of the square's sides, or as cutting the length of each side in half. Now notice what happens to that half-sized square's area when we substitute s/2 for s:

a = (s/2) ² = s²/4

While the perimeter is just divided by 2, the area is divided by 2², or 4. We can use this knowledge to find the area of the half-sized square in our problem:

a = 64/4 = 16.

So, the area of our square is 16 square units.

A square is a figure that has 4 equal sides. We also know that the perimeter is the sum of all the sides of a figure. In this case we have 4 sides each with a measure of x adding to 64in. From this information we can find out the measure of each side. Our equation follows:

x+x+x+x=64

4x=64

x=16

Now that we know that each side is 16in we can answer the question. Since we're being asked the dimensions of a square with dimensions half as large, then all we need to do is take half of 16in which is 8in.

Answer: 8in each side.