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?
3.4 cm
4.8 cm
24 cm
27 cm

Answer 1

The length of the line segment of octagon which is AB equal to 3.4 cm.

Given that the area of the regular octagon is 54 $cm^{2}$, apothem of regular octagon is 4 cm. Line segment AB is side of the octagon.

We are required to find the length of the line segment AB.

A regular octagon has eight equal sides.

Area of regular octagon=Perimeter*apothem/2-----------1

We have to put the value of area and apothem in equation 1.

54=perimeter*4/2

Perimeter=(54*2)/4

=27 cm

Perimeter=27 cm.

Now we know that the perimeter is equal to the sum of the lengths of all sides of figure. So,

Perimeter=8*side

27=8*AB

AB=27/8

=3.375 cm

After rounding off it will be equal to 3.4 cm.

Hence the length of line segment is equal to 3.4 cm.

Learn more about perimeter at https://brainly.com/question/397857

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