Question

A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.

What is the equation to find the total area of the pyramid?

What numbers go in the boxes for the blank equation.

Answer 1

The total area of pyramid is 113.569 square units

The equation to find the total area of the pyramid is Total area = base area + lateral area.

Solution:

Given, A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6.

The total area of pyramid is given by:

`A=A_(b)+A_(l)` ---- eqn 1

Where,

`A_(b) \text { is the base area and } A_(l) \text { is the lateral area }`

The area of base is given as:

`A_(b)=(3 √(3))/(2) l^(2)`

Where "l" is the side of hexagon.

Substituting we get,

`\begin{array}{l}{A_(b)=(3 √(3))/(2)(4)^(2)} \\\\ {=(3 √(3))/(2) * 16=3 √(3) * 8} \\\\ {A_(b)=24 √(3)}\end{array}`

The lateral area is given as:

`A_(l)=3 b h`

Where,

b: base of the triangle

h: height of the triangle

Substituting we get,

`\begin{array}{l}{A_(l)=3 *(4) *(6)} \\\\ {A_(l)=72}\end{array}`

Plugging in the values we found in eqn 1 we get,

`A=24 √(3)+72`

A = 113.569 square units

Summarizing the results:

The total area of pyramid is 113.569 square units approximately

The equation used to find total area of pyramid is Total area = base area + lateral area.