Question

Find the Total Surface area of a Pyramid. Its base is a regular hexagon 4cm on a side. its height is 8 cm. Round off to nearest tenth.

Answer 1

The total surface area of a regular hexagonal pyramid is 146.2 cm².

Explanation:

The base is a regular hexagon 4cm on a side. its height is 8 cm.

The total surface area of a pyramid with regular hexagon base

`A=(3√(3))/(2)a^2+3a\sqrt{h^2+(3a^2)/(4)`

Where, a represents the base edge and h represents the height of the pyramid.

The area of given regular hexagonal pyramid is

`A=(3√(3))/(2)(4)^2+3(4)\sqrt{(8)^2+(3(4)^2)/(4)`

`A=(3√(3))/(2)(16)+12√(64+12)`

`A=24√(3)+12√(76)`

`A=146.182794027`

`A=146.2`

The total surface area of a regular hexagonal pyramid is 146.2 cm².