Answer:
Total area of pyramid = 113.57 sq units
Step-by-step explanation:
Given that
Pyramid has a regular hexagonal with side, a = 4 units
Slant height = 6 units
To find: Total Area of pyramid = ?
Solution:
Total area of pyramid = Area of hexagon + Area of each triangular face
Area of hexagon is given as:
[tex]A = 6 \times \dfrac{\sqrt3}{4}a^2\\\Rightarrow A = 6 \times \dfrac{\sqrt3}{4}4^2\\\\\Rightarrow A = 41.57\ sq\ units[/tex]
There are 6 triangular faces with base = 4 units and height as 6 units.
Area of 6 triangular faces:
[tex]6 \times \dfrac{1}{2} \times Base\times Height\\\Rightarrow 6 \times \dfrac{1}{2} \times 4\times 6\\\\\Rightarrow 72\ sq\ units[/tex]
Total area of pyramid = 41.57 + 72 = 113.57 sq units
