Question

Find the total area the regular pyramid.

T. A. =

Answer 1

`T.A = 18√(91) +54√(3)`

Answer 2

Answer:
`SA=18√(91)+54√(3)`

Explanation:

You must apply the following formula for calculate the total surface area the regular pyramid:

`SA=(pl)/(2)+B`

Where p is the perimeter of the base, l is the slant height and B is the area of the base.

Find the apothem of the hexagonal base:

`a=(s)/(2tan((180)/(n)))`

Where s is the side length and n is the number of sides the polygon.

Then:

`a=(6)/(2tan((180)/(6)))`

`a=3√(3)`

Apply the Pythagorean Theorem to find the slant height:

`l=\sqrt{(3√(3))^2+8^2}=√(91)`

The perimeter is:

`p=s*6=6*6=36`

The area of the base is:

`B=(3√(3)*s^2)/(2)`

Where s is the side length.

Then:

`B=s^2((3√(3))/(2))=54√(3)`

Susbtituting values, you obtain:

`SA=(36*√(91))/(2)+54√(3)`

`SA=18√(91)+54√(3)`