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:
[tex]A=A_{b}+A_{l}[/tex] ---- eqn 1
Where,
[tex]A_{b} \text { is the base area and } A_{l} \text { is the lateral area }[/tex]
The area of base is given as:
[tex]A_{b}=\frac{3 \sqrt{3}}{2} l^{2}[/tex]
Where "l" is the side of hexagon.
Substituting we get,
[tex]\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}[/tex]
The lateral area is given as:
[tex]A_{l}=3 b h[/tex]
Where,
b: base of the triangle
h: height of the triangle
Substituting we get,
[tex]\begin{array}{l}{A_{l}=3 \times(4) \times(6)} \\\\ {A_{l}=72}\end{array}[/tex]
Plugging in the values we found in eqn 1 we get,
[tex]A=24 \sqrt{3}+72[/tex]
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.
