Question

the window is shaped like an equilateral triangle side length of 16 ft if Glass cost $20.25 per square foot how much will the replacement window cost

Answer 1

The Area of an Equilateral Triangle with side length s is given as:

`A=\frac{\sqrt[]{3}}{4}s^2`

Substitute s=16 into the equation:

`\begin{gathered} A=\frac{\sqrt[]{3}}{4}(16)^2=\frac{\sqrt[]{3}*16*16}{4} \\ A=\frac{\sqrt[]{3}*\cancel{16}^4*16}{\cancel{4}^1}=\sqrt[]{3}*4*16\approx110.85\text{ square feet} \end{gathered}`

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:

`\begin{gathered} 110.85\/ft^2*\$20.25\/ft^2 \\ \approx\$2244.71 \end{gathered}`

The cost of the replacement window is about $2,244.71