Assign variables such that

One side of ABCD = a

and One side of EFGH = e

Note that all sides are the same in a square. Since the perimeter is the sum of all sides, according to the question:

4a = 3 x 4e = 12e or a = 3e

From that area of EFGH is 25,

e x e = 25 so e = 5

Substitute a = 3e so a = 15

We aren’t done. Since we were asked for the area of ABCD, this is a x a = 225.

Let S be the original side length. S*S would represent the original area. Doubling the side length would give you 2S*2S, simplifying to 4*(S*S), giving a new area of 4x the original, or 144.

Area of a square in terms of each of its sides:

  Area = S x S

Perimeter of a square:

  Perimeter = 4S

So if 'the perimeter of a square is equal to twice its area':

  2 x Area = Perimeter

  2 x [S x S] = [4S]; divide by 2:

  S x S = 2S; divide by S:

  S = 2

If Freddie uses x feet of fencing makes a square, each side must be x/4 feet long. The area of this square is (x/4)² = x²/16 = p square feet.

If Freddie uses one third of x feet of fencing makes a square, each side must be x/12 feet long. The area of this square is (x/12)² = x²/144 = 1/9(x²/16) = 1/9(p) = p/9 square feet.

Alternate method:

The scale factor between the small perimeter and the larger perimeter = 1 : 3. Since we're comparing area, a two-dimensional measurement, we can square the scale factor and see that the ratio of the areas is 1² : 3² = 1 : 9.

This is an isosceles right triangle, so the diagonal must equal times the length of a side. Thus, one side of the square measures , and the area is equal to 

The area of  is , the area of  is . Therefore, you can fit 5.06  in .

The perimeter of a square is given by  so the side length of the original square is   The side of the new square is enlarged by a factor of 3 to give  

So the area of the new square is given by .

The area of a circle is given by A = πr² or 22/7r²

The area of a square is given by A = s² or (2r)² = 4r²

Then subtract the area of the circle from the area of the square and get 6/7 square units.

Since the square's perimeter is 44, then each side is .

Then in order to find the area, use the definition that the

Assume that the length of each midpoint is 1.  This means that the length of each side of the large square is 2, so the area of the larger square is 4 square units.

To find the area of the smaller square, first find the length of each side.  Because the length of each midpoint is 1, each side of the smaller square is  (use either the Pythagorean Theorem or notice that these right trianges are isoceles right trianges, so  can be used).  

The area then of the smaller square is 2 square units.

Comparing the area of the two squares, the larger square is 2 times larger than the smaller square.