Answer:
(177.94 ± 3.81) cm^2
Explanation:
l + Δl = 21.7 ± 0.2 cm
b + Δb = 8.2 ± 0.1 cm
Area, A = l x b = 21.7 x 8.2 = 177.94 cm^2
Now use error propagation
[tex]\frac{\Delta A}{A}=\frac{\Delta l}{l}+\frac{\Delta b}{b}[/tex]
[tex]\frac{\Delta A}{A}=\frac{0.2}{21.7}+\frac{0.1}{8.2}[/tex]
[tex]\Delta A=177.94 \times \left ( 0.0092 + 0.0122 \right )=3.81[/tex]
So, the area with the error limits is written as
A + ΔA = (177.94 ± 3.81) cm^2
