Question

This regular octagon table allows each person to grill their own food.The outer perimeter of the table is 24 feet and has an apothem length of3.62 feet. Each side of the outer edge of the grilling area is 1.5 feet, with aapothem length of 1.81 feet. How much space does each person at thetable have for their eating area? *

Answer 1

Given data:

The outerperimeter of the regular ocatgon table , P=24feet.

The apotherm length of the regular ocatgon table, l=3.62 feet.

The length of each side of the grilling area in the shape of a regular octagon, a=1.5 feet.

The apotherm length of grilling area, l'=1.81 feet.

A regular ocatgon has 8 equal sides.

Hence, the perimeter of the grilling area having the shape of a regular octagon is,

$P^{\prime}=8a=8\times1.5=12\text{ f}eet$

Now, the area of the grilling area is,

$\begin{gathered} A^{\prime}=\frac{1}{2}P^{\prime}l^{\prime} \\ =\frac{1}{2}\times12\times1.81 \\ =10.86ft^2 \end{gathered}$

The area inside the outer edge of the regular octagon table is,

$\begin{gathered} A=\frac{1}{2}Pl \\ =\frac{1}{2}\times24\times3.62 \\ =43.44ft^2 \end{gathered}$

Now, the area of the eating space in the table is,

$\begin{gathered} A_1=A-A^{\prime} \\ =43.44-10.86 \\ =32.58ft^2 \end{gathered}$

Now, the area of the space that each person have as the eating area is,

$\begin{gathered} A_{\text{each person}}=\frac{A_1}{8} \\ =\frac{32.58}{8} \\ =4.0725ft^2 \end{gathered}$

Therefore, each person has a space of 4.0725 ft^2 at the table for their eating area.