Question

1. what is the side length of a square with an area of 3 square units? 9. practice find the areas of the following perfect squares. side length 1 2 3 4 5 6 7 8 9 10 11 12 13 area 10. practice the area of each square is given. find an exact value for the length of a side of each square. a. a = 14 cm² b. a = 20 cm²

Explanation:

Step1: Recall area formula for square

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

Step2: Solve for side - length when $A = 3$

If $A = s^{2}=3$, then $s=\sqrt{3}$ units.

Step3: For side - length of square with $A = 14\ cm^{2}$

Using $A = s^{2}$, when $A = 14$, then $s=\sqrt{14}\ cm$.

Step4: For side - length of square with $A = 20\ cm^{2}$

Using $A = s^{2}$, when $A = 20$, then $s=\sqrt{20}=2\sqrt{5}\ cm$.

Step5: Calculate areas for perfect squares

For a square with side - length $s = 1$, $A=s^{2}=1\times1 = 1$ square unit.
For $s = 2$, $A=s^{2}=2\times2 = 4$ square units.
For $s = 3$, $A=s^{2}=3\times3 = 9$ square units.
For $s = 4$, $A=s^{2}=4\times4 = 16$ square units.
For $s = 5$, $A=s^{2}=5\times5 = 25$ square units.
For $s = 6$, $A=s^{2}=6\times6 = 36$ square units.
For $s = 7$, $A=s^{2}=7\times7 = 49$ square units.
For $s = 8$, $A=s^{2}=8\times8 = 64$ square units.
For $s = 9$, $A=s^{2}=9\times9 = 81$ square units.
For $s = 10$, $A=s^{2}=10\times10 = 100$ square units.
For $s = 11$, $A=s^{2}=11\times11 = 121$ square units.
For $s = 12$, $A=s^{2}=12\times12 = 144$ square units.
For $s = 13$, $A=s^{2}=13\times13 = 169$ square units.

Answer:

• Side - length of square with area 3 square units: $\sqrt{3}$ units
• Areas of perfect squares:

Side length	Area
2	4 square units
3	9 square units
4	16 square units
5	25 square units
6	36 square units
7	49 square units
8	64 square units
9	81 square units
10	100 square units
11	121 square units
12	144 square units
13	169 square units

• Side - length of square with area 14 $cm^{2}$: $\sqrt{14}$ cm
• Side - length of square with area 20 $cm^{2}$: $2\sqrt{5}$ cm