Question

A rectangle plot of land has dimensions a= 100 +/- 1m, b= 153 +/- 2m, c= 102 +/- 3m and d= 151+/- 2,. What is the perimeter AND area of this plot, give value and uncertainty. If you could please explain steps too that would be amazing.

Answer 1

given
a = 100 +- 1 m = A + dA
b = 153 +- 2 m = B + dB
c = 102 +- 3m = C + dC
d = 151 +- 2 m = D + dD

now, area of this land is A = average length * average breadth
Area = (a + c)/2 * (b + d)/2 = (a + c)(b + d)/4
so Area = (A + C)(B + D)/4
error in area = area*(error in length/average length + error in breadth/average breadth)
error in length = dA + dC
error in breadh = dB + dD

hence
area = 15352 m^2
error in area = 4/101 + 4/152 =1012 m^2
hence
final area = 15352 +- 1012 m^2

similiarly final perimeter = A + B + C + D +- (dA + dB + dC + dD) = 506 +- 8 m