Answer:
122.2 in^2.
Step-by-step explanation:
WE can divide a regular octagon into 8 triangles with height ( = the apotherm) = 6.5 and base = 4.7.
The area of each triangle is 1/2 * 4.7 *6.5 so #the area of the octagon
= 8 * 1/2 * 4.7 * 6.5
= 122.2 in^2.
For this case we have by definition, that the area of an octagon is given by:
[tex]A = \frac {p * a} {2}[/tex]
Where:
p: perimeter
a: apothem
We have that the perimeter is given by the sum of the sides of the octagon:
[tex]p = 8 * 4.7 = 37.6 \ in\\a = 6.5 \ in[/tex]
Substituting:
[tex]A = \frac {37.6 * 6.5} {2} = 122.2[/tex]
So, the area of the octagon is[tex]122.2 \ in ^ 2[/tex]
Answer:
[tex]122.2 \ in ^ 2[/tex]
