Question
whats the area of a square with diaglal measures of 12
Answers
GPT-4o mini
To find the area of a square when you know the length of the diagonal, you can use the relationship between the diagonal \( d \) and the side length \( s \) of the square. The formula for the diagonal of a square is given by:
\[
d = s\sqrt{2}
\]
If the diagonal \( d \) is 12, you can rearrange this formula to find the side length \( s \):
\[
s = \frac{d}{\sqrt{2}} = \frac{12}{\sqrt{2}} = 12 \cdot \frac{\sqrt{2}}{2} = 6\sqrt{2}
\]
Now, to find the area \( A \) of the square, you use the formula:
\[
A = s^2
\]
Substituting the value of \( s \):
\[
A = (6\sqrt{2})^2 = 36 \cdot 2 = 72
\]
Therefore, the area of the square is \( 72 \) square units.
\[
d = s\sqrt{2}
\]
If the diagonal \( d \) is 12, you can rearrange this formula to find the side length \( s \):
\[
s = \frac{d}{\sqrt{2}} = \frac{12}{\sqrt{2}} = 12 \cdot \frac{\sqrt{2}}{2} = 6\sqrt{2}
\]
Now, to find the area \( A \) of the square, you use the formula:
\[
A = s^2
\]
Substituting the value of \( s \):
\[
A = (6\sqrt{2})^2 = 36 \cdot 2 = 72
\]
Therefore, the area of the square is \( 72 \) square units.