Luguin
A right pyramid with a regular hexagon base has a
height of 3 units.
If a side of the hexagon is 6 units long, then the
apothem is v3 units long.
The slant height is the hypotenuse of a right triangle
formed with the apothem and the
Using the Pythagorean theorem c= Vo? + b2 to find the
slant height results in a slant height of units.
The lateral area is square units.

Step-by-step explanation:

Given

A right regular hexagonal pyramid with ...

Find

Solution

a) The apothem (a) and height (b) of the pyramid are two legs of the right triangle having the slant height as its hypotenuse (c). The Pythagorean theorem tells us the relationship is ...

  c = √(a² +b²) = √((3√3)² +3²) = √(27+9) = √36

  c = 6

The slant height of the pyramid is 6 units.

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b) The lateral surface area of the pyramid is the area of each triangular face, multiplied by the number of faces. The area of one face will be ...

  A = (1/2)bh = (1/2)(6 units)(6 units) = 18 units²

Then the lateral surface area is 6 times this value:

  SA = 6(18 units²) = 108 units²

The lateral surface area of the pyramid is 108 square units.