Determine the area of square.
[tex]\begin{gathered} A_1=20\cdot20 \\ =400 \end{gathered}[/tex]
The side of octagon is 8.
Determine the base length or height of a triangle.
[tex]\begin{gathered} 2h=20-8 \\ h=\frac{12}{2} \\ =6 \end{gathered}[/tex]
So height and base of triangle is equal to h = 6 and b = 6 respectively.
Determine the area of 4 triangle.
[tex]\begin{gathered} A_2=4\times\frac{1}{2}\cdot b\cdot h \\ =4\times\frac{1}{2}\cdot6\cdot6 \\ =72 \end{gathered}[/tex]
Determine the area of octagon by substract area of 4 triangles from area of square.
[tex]\begin{gathered} A=A_2-A_1 \\ =400-72 \\ =328 \end{gathered}[/tex]
Thus area of octahedral room is 328 square feet.
