Answer:
The Exact area of the Octagon is 82 square inches;
[tex]A=82in^2[/tex]Explanation:
From the attached image we can find the exact area of the octagon by extending to form a square and four triangles;
The area of the octagon is the area of the square minus the area of the four triangles at the corners of the square.
Area of a square is;
[tex]A_1=l^2[/tex]Area of each triangle;
[tex]A_t=\frac{1}{2}bh[/tex]the area of the four triangles are;
[tex]\begin{gathered} A_2=4\times\frac{1}{2}bh \\ A_2=2bh \end{gathered}[/tex]The area of the octagon is;
[tex]\begin{gathered} A=A_1-A_2 \\ A=l^2-2bh \end{gathered}[/tex]From the diagram;
h = 3 in
b = 3 in
l = 10 in
Substituting the values we have;
[tex]\begin{gathered} A=A_1-A_2 \\ A=l^2-2bh \\ A=10^2-2(3\times3) \\ A=100-18 \\ A=82in^2 \end{gathered}[/tex]The Exact area of the Octagon is 82 square inches;
[tex]A=82in^2[/tex]
