Chapter 11.1, Problem 16PSC

To determine

To find : The area of the rectangle to the nearest tenth

Answer to Problem 16PSC

The area of the rectangle is $249.4$

Explanation of Solution

Given information : The following information has been given

Side of the regular hexagon is $l=12$

Diagonals are the sides of the rectangle

Formula used : The area of any rectangle will be

  $A=(length)(width)$

Calculation : We know that if the side of the hexagon is $12$ , then the length of the diagonal can be calculated as

  $d=2(12\sin {60}^0)=12\sqrt{3}$

Now, we know that the area of this rectangle can be found as

  $A=(length)(diagonal)=l\times d$

Hence, substituting the values of $l=12$ and $d=12\sqrt{3}$ , we get

  $A=(12\sqrt{3})(12)=144\sqrt{3}=249.42$