A man owns a rectangular piece of land. The land is divided into four rectangular pieces, known as Region A, Region B, Region C, and Region D. One day his daughter, Nancy, asked him, what is the area of our land? The father replied: I will only tell you that the area of Region B is 200 ft^2 larger than the area of Region A; the area of Region C is 400 ft^2 larger than the area of Region B; and the area of Region D is 800 ft^2 larger than area of Region C. What answer to her question will Nancy derive from her father’s statement?

A = X Ft^2

B = (X+200) Ft^2
C = (X+200) +400 Ft^2
D = (X+200)+400 + 800

AREA = 4x + 600 + 800 + 800 =
4x + 2200 = 4A + 2200

Answer: She must measure Region A,
multiply the results by 4, and add 2200
Ft^2.

To find the area of the entire land, we need to calculate the areas of Region A, Region B, Region C, and Region D separately and then add them together.

According to the father's statement:
- The area of Region B is 200 ft^2 larger than the area of Region A.
- The area of Region C is 400 ft^2 larger than the area of Region B.
- The area of Region D is 800 ft^2 larger than the area of Region C.

Let us assume the area of Region A as 'a' ft^2.

Based on the given information, we can derive the following relations:

Area of Region B = Area of Region A + 200 ft^2
Area of Region C = Area of Region B + 400 ft^2
Area of Region D = Area of Region C + 800 ft^2

Substituting the derived relations, we get:

Area of Region B = a + 200 ft^2
Area of Region C = (a + 200 ft^2) + 400 ft^2 = a + 600 ft^2
Area of Region D = (a + 600 ft^2) + 800 ft^2 = a + 1400 ft^2

To find the total area of the land, we sum up the areas of all four regions:

Total Area = Area of Region A + Area of Region B + Area of Region C + Area of Region D
= a + (a + 200 ft^2) + (a + 600 ft^2) + (a + 1400 ft^2)
= 4a + 2200 ft^2

So, Nancy can derive from her father's statement that the area of their land is 4a + 2200 ft^2, where 'a' represents the unknown area of Region A.