Question

18. Find the height and the volume of a regular hexagonalpyramid with lateral edges 10 ft and base edges 6 ft.

Answer 1

Step 1

`Volume\text{ of a pyramid = }(1)/(3)*\text{ Base area }*\text{ Height}`

Ste 2:

Use the formula below to find the base area of the regular hexagon

`\begin{gathered} \text{Base area = }(3)/(2)√(3)\text{ s}^2 \\ \text{s = length of base edges = 6 ft} \end{gathered}`

Step 3

`\begin{gathered} Base\text{ area = }(3)/(2)*√(3)\text{ }*\text{ 6}^2 \\ \text{= 93.5 ft}^2 \end{gathered}`

Step 4

The height of the pyramid can be found using Pythagorean's Theorem

`\text{Height = }√(10^2-6^2)\text{ = }\sqrt{100-\text{ 36}}\text{ = }√(64)\text{ = 8 ft}`

Step 5

The volume is calculated below.

`\begin{gathered} \text{Volume = }(1)/(3)\text{ }*\text{ base area }*\text{ height} \\ \text{= }(1)/(3)\text{ }*\text{ 93.5 }*8 \\ \text{= 249.3333333 ft}^3 \end{gathered}`

Final answer

`144√(3)\text{ or 249.4153163}`