Question

determine if there is a proportional relationship between the length of the diagonals and the areas of the squares.

square (cm)	side lengths (cm)	area (cm²)
b	5.1
c	5.5
d	6

Explanation:

Step1: Recall area formula for square

The area formula of a square is $A = s^{2}$, where $s$ is the side - length of the square.

Step2: Calculate area of square A

For square A with $s = 4.1$ cm, $A_A=4.1^{2}=16.81$ $cm^{2}$.

Step3: Calculate area of square B

For square B with $s = 5.1$ cm, $A_B = 5.1^{2}=26.01$ $cm^{2}$.

Step4: Calculate area of square C

For square C with $s = 5.5$ cm, $A_C=5.5^{2}=30.25$ $cm^{2}$.

Step5: Calculate area of square D

For square D with $s = 6$ cm, $A_D=6^{2}=36$ $cm^{2}$.

Answer:

Square (cm)	Side lengths (cm)	Area ($cm^{2}$)
B	5.1	26.01
C	5.5	30.25
D	6	36