Chapter 11.4, Problem 27PPS

To determine

To find: The area of the figure with the given dimension.

Answer to Problem 27PPS

The required area of the region is $1438.3{\text{mm}}^2$ .

Explanation of Solution

Given:

The rectangular hexagon with the side length of 30 mm then, the square that is shared with one of its side removed from the interior of the hexagon.

Calculation:

Consider the area of the hexagon has the side $a=\frac{3\sqrt{3}}{2}{s}^2$ . Then,

  $\begin{array}{c}A=\frac{3\sqrt{3}}{2}{\left(30\right)}^2\\ =2338.3{\text{mm}}^2\end{array}$

The area of the square with the side $x$ is,

  $\begin{array}{c}A=x^2\\ ={30}^2\\ =900{\text{mm}}^2\end{array}$

Then, the required area of the region is,

  $2383.3{\text{mm}}^2-900{\text{mm}}^2=1438.3{\text{mm}}^2$