Chapter 11.2, Problem 42STP

To determine

To find:

The height of each triangle.

Answer to Problem 42STP

The option B is correct.

Explanation of Solution

Given information:

A regular hexagon is divided into $6$ congruent triangles. If the perimeter of the hexagon is $48$ centimeters.

Calculation:

Perimeter is the sum of all sides of a polygon.

A regular hexagon has $6$ sides.

Assume that the side be $a\text{ cm}$ .

So, the required perimeter is as follows:

  $P=6a$

Substitute $P=48$ in the above to find the side.

  $\begin{array}{c}6a=48\\ a=\frac{48}{6}\\ =8\end{array}$

Therefore, the side of each triangle which is in the form of equilateral is $8\text{ cm}$ .

Height of the equilateral triangle is:

  $h=a\frac{\sqrt{3}}{2}$

Substitute $a=8$ in the above to find the height of the triangle.

  $\begin{array}{c}h=a\frac{\sqrt{3}}{2}\\ =\frac{8\sqrt{3}}{2}\\ =4\sqrt{3}\end{array}$

Hence, the option B is correct.