Question

The area of the regular octagon is approximately 54 cm2. A regular octagon has an apothem with length 4 centimeters and an area of 54 centimeters squared. Line segment A B is a side of the octagon. What is the length of line segment AB, rounded to the nearest tenth? a) 3.4 cm b) 4.8 cm c) 24 cm d) 27 cm

Answer 1

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,

$\textrm{area of regular octagon}=\textrm{Perimeter}\times \frac{Apothem}{2}$

substituting the given values in equation we get

$54 = Perimter\times \frac{4}{2}\\ \\\therefore Perimeter=\frac{54}{2}\\ \\\therefore Perimeter = 27\ cm$

Now,

     Perimeter = 8 × Side

∴    Perimeter = 8 × AB

∴               27  = 8 × AB

∴    $AB =\frac{27}{8}\\ \\\therefore AB =3.375\ cm$

After rounded to nearest 10th we get

AB =3.4 cm

The length of line segment AB = 3.4 cm.

Answer 2

Answer:

the answer is A