Question

1. copy each square on grid paper.

find its area.
then write the side length of the square.
a)
b)

Explanation:

Step1: <A Short Explanation of the Step>

For part a)
Let's assume the side - length of each small square on the grid paper is \(1\) unit.
We can use the formula for the area of a square \(A = s^{2}\), but for a rotated square (diamond - shaped in the grid), we can also use the formula \(A=\text{base}\times\text{height}\) or count the number of unit squares. Another way is to use the formula \(A = \frac{1}{2}\times d_{1}\times d_{2}\) (where \(d_{1}\) and \(d_{2}\) are the lengths of the diagonals).
The diagonals of the square in part a) are \(d_{1}=4\) and \(d_{2}=4\).

$$A=\frac{1}{2}\times d_{1}\times d_{2}=\frac{1}{2}\times4\times4 = 8$$

If \(A = s^{2}\), then \(s^{2}=8\), and \(s=\sqrt{8}=2\sqrt{2}\)

Step2: <A Short Explanation of the Step>

For part b)
The diagonals of the square in part b) are \(d_{1}=6\) and \(d_{2}=6\)

$$A=\frac{1}{2}\times d_{1}\times d_{2}=\frac{1}{2}\times6\times6=18$$

If \(A = s^{2}\), then \(s^{2}=18\), and \(s = \sqrt{18}=3\sqrt{2}\)

Answer:

a) Area \(A = 8\) square units, side - length \(s=2\sqrt{2}\) units
b) Area \(A = 18\) square units, side - length \(s = 3\sqrt{2}\) units