#### Setback area for various shapes if area inside shape and setback distance are held constant

We will consider a circle, a square, a nearly square rectangle, and a very tall thin rectangle. In every case, the basic shape will contain 1,000 Acres (42,560,000 Sq Ft) and we will determine area of a 100 foot setback.

## Circle

radius * radius * 3.1415926535 = area

42,560 Sq Ft = 1 Acre

1000 Acres * 43,560 SqFt/Acre = 43,560,000 Sq Ft

radius of 1,000 Acre Circle = SquareRoot(43,560,000 Sq Ft / 3.1415926535) = 3,680.7 FT

### Calculations with 100 Foot Setback

If we add 100 Ft for setback the total area = 3,680.7 Ft + 100 Ft = 3,780.7 Feet

Total Sq Ft with 100 Ft setback = 3,780.7 Ft * 3,780.7 Ft * 3.1415926535 = 44,904,044 Sq Ft

Total Acres with 100 Ft setback = 44,904,044 Sq Ft / 42,560 Sq Ft per Acre = 1,055.1 Acres

Setback Land not paying higher local real estate property tax = 1,055.1 Total – 1000 Acres = 55.1 Acres

## Square

width * length = area

SqRt of 43,560,000 Sq Ft = 6524 Ft

Per-meter = side length + side length + width length + width length

or

Peremeter = 6,524 + 6,524 + 6,524 + 6,524 = 26,095 ft

Setback area of 100 ft along width and length = 26,095 Ft* 100 Ft = 2,609,500 Sq Ft = 61.3 Acre

But we also need the area of setback at all 4 corners, which is the area of a circle with radius = the setback. (We need a complete circle because 1/4 of it will be at each corner.)

Area of 100 ft circle = 100 * 100 * 3.1415926535 = 31,416 Sq Ft = 3,680.7 FT = 0.7 Acre

Total setback area for a 1000 acre square when setback is 100 foot buffer on outside of square = 62.1

## Nearly Square Rectangle

width * length = area

8,000 Ft * 5,320 Ft = 42,560,000 Sq Ft

Perimeter = side length + side length + width length + width length

or

Perimeter = 8,000 + 8,000 + 5,320 + 5,320 = 26,640 ft

Setback area of 100 ft along width and length = 26,640 Ft* 100 Ft = 2,664,000 Sq Ft = 62.6 Acre

But we also need the area of setback at all 4 corners, which is the area of a circle with radius = the setback. (We need a complete circle because 1/4 of it will be at each corner.)

Area of 100 ft circle = 100 * 100 * 3.1415926535 = 31,416 Sq Ft = 3,680.7 FT = 0.7 Acre

Total setback area for a 1000 acre nearly square rectangle when setback is 100 foot buffer on outside of nearly square rectangle = 63.3 Acres

## Long Narrow Rectangle

width * length = area

80 Ft * 5,52000 Ft = 42,560,000 Sq Ft

Perimeter = side length + side length + width length + width length

or

Perimeter = 80 + 80 + 552,000 + 552,000 = 1,064,160 ft

Setback area of 100 ft along width and length = 1,064,160 Ft * 100 Ft = 106,416,000 Sq Ft = 2,500.4 Acre

But we also need the area of setback at all 4 corners, which is the area of a circle with radius = the setback. (We need a complete circle because 1/4 of it will be at each corner.)

Area of 100 ft circle = 100 * 100 * 3.1415926535 = 31,416 Sq Ft = 3,680.7 FT = 0.7 Acre

Total setback area for a 1000 acre square when setback is 100 foot on outside of square = 2,501.1