Question

2. They have a regular pyramid with a regularhexagonal base measuring 3 cm and a height of4 cm.A. Build that regular pyramid.B. Calculate all its area

Answer 1

The side length of the hexagonal base is

`a=3cm`

The height of the pyramid is

`h=4cm`

To build the pyramid, we will have the image below

PART B:

To calculate the area of the hexagonal pyramid, we will use the formula below

`\begin{gathered} A=(3√(3))/(2)a^2+3a\sqrt{h^2+(3a^2)/(4)} \\ A=(3√(3))/(2)*9+3(3)\sqrt{(4^2)+(3(9))/(4)} \\ A=(27√(3))/(2)+9\sqrt{16+(27)/(4)} \\ A=(27√(3))/(2)+9\sqrt{(64+27)/(4)} \\ A=(27√(3))/(2)+9\sqrt{(91)/(4)} \\ A=(27√(3)+9√(91))/(2) \\ A=66.31cm^2 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} A=(3√(3))/(2)a^2+3a\sqrt{h^2+(3a^2)/(4)} \\ A=(3√(3))/(2)*3^2+3(3)\sqrt{4^2+(3(3)^2)/(4)} \\ A=66.31cm^2 \end{gathered}`

Hence,

The area of the hexagonal based pyramid is

`\Rightarrow A=66.31cm^2`