Answer:
The area of an octagon whose perimeter is 120 cm is 1086.4 [tex]cm^{2}[/tex]
Step-by-step explanation:
An octagon is a polygon with eight sides. If the lengths of all the sides and the measurement of all the angles are equal, the octagon is called a regular octagon.
There is a predefined set of formulas for the calculation of perimeter, and area of a regular octagon.
The perimeter of an Octagon is given by
[tex]P=8a[/tex]
and the area of an Octagon is given by
[tex]A=2a^{2}(1+\sqrt{2})[/tex]
We know that the perimeter is 120 cm, solving for side length (a) in the perimeter formula we get
[tex]120=8a\\\frac{8a}{8}=\frac{120}{8}\\a=15[/tex]
Now, we calculate the area
[tex]A=2a^{2}(1+\sqrt{2})\\A=2(15)^{2}(1+\sqrt{2})\\A=450\left(1+\sqrt{2}\right)\\A\approx 1086.4 \:cm^{2}[/tex]
