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.T. A. =The answer has to be answered in the format below TA .

Answer 1

Given:

Slant = 6

a = side lenght = 4

Apply : area of an hexagon

`A=\frac{3\sqrt[\placeholder{⬚}]{3}}{2}a^2`

Where:

A = area

Replacing:

`A=\frac{3\sqrt[\placeholder{⬚}]{3}}{2}(4)^2=24\sqrt[\placeholder{⬚}]{3}\text{ square units}`

Now, the lateral face of the pyramid is a triangle , base = 4 , height = 6

An Hexagon has 6 triangular faces.

Area of a triangle = 1/2 bh

LA = 6 x 1/2 x 4 x 6 = 72 square units

Total area (TA) = A + LA = 24 √3 + 72 square units

Answer: 72 + 24 √3