Answer:
The length of line segment AB = 3.4 cm.
Step-by-step explanation:
Given:
The area of the regular octagon is approximately = 54 cm²
A regular octagon has an apothem with length = 4 cm
AB = side of the octagon
To Find:
AB = side of the octagon = ?
Solution:
A regular octagon has an Eight equal Side
We Know that,
[tex]\textrm{area of regular octagon}=\textrm{Perimeter}\times \frac{Apothem}{2}[/tex]
substituting the given values in equation we get
[tex]54 = Perimter\times \frac{4}{2}\\ \\\therefore Perimeter=\frac{54}{2}\\ \\\therefore Perimeter = 27\ cm\\[/tex]
Now,
Perimeter = 8 × Side
∴ Perimeter = 8 × AB
∴ 27 = 8 × AB
∴ [tex]AB =\frac{27}{8}\\ \\\therefore AB =3.375\ cm\\\\[/tex]
After rounded to nearest 10th we get
AB =3.4 cm
The length of line segment AB = 3.4 cm.
