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

Answer:

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

Step-by-step 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

$A=\frac{3\sqrt{3}}{2}a^2+3a\sqrt{h^2+\frac{3a^2}{4}$

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

The area of given regular hexagonal pyramid is

$A=\frac{3\sqrt{3}}{2}(4)^2+3(4)\sqrt{(8)^2+\frac{3(4)^2}{4}$

$A=\frac{3\sqrt{3}}{2}(16)+12\sqrt{64+12}$

$A=24\sqrt{3}+12\sqrt{76}$

$A=146.182794027$

$A=146.2$

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