Chapter 11.5, Problem 4PSA

a

To determine

To calculate : The area of the regular hexagon with side length $6$

Answer to Problem 4PSA

The area is $A=93.5$

Explanation of Solution

Given information : The side of the regular hexagon is, $a=6$

Formula used : We use the following formula to find the area of a regular hexagon

  $A=\frac{3\sqrt{3}}{2}{a}^2$

Calculation : Substituting the value of $a=6$ in the equation, we get

  $\begin{array}{l}$ A=\frac{3\sqrt{3}}{2}{(6)}^2$A=54\sqrt{3}\end{array}$

Thus, we get

  $A=54\sqrt{3}=93.53$

b

To determine

To calculate : The area of the regular hexagon with side length $8$

Answer to Problem 4PSA

The area is $A=166.3$

Explanation of Solution

Given information :

The side of the regular hexagon is, $a=8$

Formula used : We use the following formula to find the area of an regular hexagon

  $A=\frac{3\sqrt{3}}{2}{a}^2$

Calculation : Substituting the value of $a=8$ in the equation, we get

  $\begin{array}{l}$ A=\frac{3\sqrt{3}}{2}{(8)}^2$A=96\sqrt{3}\end{array}$

Thus, we get

  $A=96\sqrt{3}=166.28$

c

To determine

To calculate : The area of the regular hexagon with apothem $6$

Answer to Problem 4PSA

The area is $A=124.7$

Explanation of Solution

Given information : The apothem of the regular hexagon is, $h=6$

Formula used : We use the following formula to find the area of an regular hexagon

  $A=\left(2\sqrt{3}\right)h^2$

Calculation : Substituting the value of $h=3$ in the equation, we get

  $\begin{array}{l}A=\left(2\sqrt{3}\right)6^2\\ A=72\sqrt{3}\end{array}$

Thus, we get

  $A=72\sqrt{3}=124.71$

d

To determine

To calculate : The area of the regular hexagon with apothem $8$

Answer to Problem 4PSA

The area is $A=55.4$

Explanation of Solution

Given information : The apothem of the regular hexagon is, $h=8$

Formula used : We use the following formula to find the area of an regular hexagon

  $A=\left(2\sqrt{3}\right)h^2$

Calculation : Substituting the value of $h=2\sqrt{3}$ in the equation, we get

  $\begin{array}{l}A=\left(2\sqrt{3}\right)8^2\\ A=32\sqrt{3}\end{array}$

Thus, we get

  $A=32\sqrt{3}=55.43$