Question

a picture of a square floor tile is shown. the diagonal of the tile measures 12 inches. what is the area of the tile? a. 36 in² b. 72 in² c. 144 in² d. 288 in²

Explanation:

Step1: Recall the relationship between the diagonal and side of a square

For a square with side length \( s \) and diagonal \( d \), by the Pythagorean theorem, \( d^{2}=s^{2}+s^{2}=2s^{2} \).

Step2: Find the area of the square

The area of a square \( A = s^{2} \). From \( d^{2}=2s^{2} \), we can rewrite it as \( s^{2}=\frac{d^{2}}{2} \). Given \( d = 12 \) inches, substitute \( d \) into the formula: \( A=\frac{12^{2}}{2}=\frac{144}{2} = 72 \) square inches.

Answer:

B. \( 72\ \text{in}^2 \)