Question

FIND THE EXACT AREA OF THE OCTAGON. SHOW THE REASON.

Answer 1

The Exact area of the Octagon is 82 square inches;

`A=82in^2`

Step-by-step 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;

`A_1=l^2`

Area of each triangle;

`A_t=(1)/(2)bh`

the area of the four triangles are;

`\begin{gathered} A_2=4*(1)/(2)bh \\ A_2=2bh \end{gathered}`

The area of the octagon is;

`\begin{gathered} A=A_1-A_2 \\ A=l^2-2bh \end{gathered}`

From the diagram;

h = 3 in

b = 3 in

l = 10 in

Substituting the values we have;

`\begin{gathered} A=A_1-A_2 \\ A=l^2-2bh \\ A=10^2-2(3*3) \\ A=100-18 \\ A=82in^2 \end{gathered}`

The Exact area of the Octagon is 82 square inches;

`A=82in^2`