The Area of an Equilateral Triangle with side length s is given as:
[tex]A=\frac{\sqrt[]{3}}{4}s^2[/tex]
Substitute s=16 into the equation:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}(16)^2=\frac{\sqrt[]{3}\times16\times16}{4} \\ A=\frac{\sqrt[]{3}\times\cancel{16}^4\times16}{\cancel{4}^1}=\sqrt[]{3}\times4\times16\approx110.85\text{ square feet} \end{gathered}[/tex]
The area of the window is about 110.85 ft².
Since it is given that glass costs $20.25 per square foot, it follows that the replacement will cost:
[tex]\begin{gathered} 110.85\/ft^2\times\$20.25\/ft^2 \\ \approx\$2244.71 \end{gathered}[/tex]
The cost of the replacement window is about $2,244.71
