Question

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

Answer 1

Answer:

The Exact area of the Octagon is 82 square inches;

$A=82in^2$

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;

$A_t=\frac{1}{2}bh$

the area of the four triangles are;

$\begin{gathered} A_2=4\times\frac{1}{2}bh \\ A_2=2bh \end{gathered}$

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;

$\begin{gathered} A=A_1-A_2 \\ A=l^2-2bh \\ A=10^2-2(3\times3) \\ A=100-18 \\ A=82in^2 \end{gathered}$

The Exact area of the Octagon is 82 square inches;

$A=82in^2$