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.

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:

$A_{b}=\frac{3 \sqrt{3}}{2} l^{2}$

Where "l" is the side of hexagon.

Substituting we get,

$\begin{array}{l}{A_{b}=\frac{3 \sqrt{3}}{2}(4)^{2}} \\\\ {=\frac{3 \sqrt{3}}{2} \times 16=3 \sqrt{3} \times 8} \\\\ {A_{b}=24 \sqrt{3}}\end{array}$

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,

$\begin{array}{l}{A_{l}=3 \times(4) \times(6)} \\\\ {A_{l}=72}\end{array}$

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

$A=24 \sqrt{3}+72$

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.