Question

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?

Answer 1

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. 

Answer 2

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.