Question

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.

Answer 1

If a side of the hexagon is 6 units long, then the apothem is

3√3 units long.

The slant height is the hypotenuse of a right triangle formed with the apothem and the

height of the pyramid

Using the Pythagorean theorem c = to find the slant height results in a slant height of

6 units.

The lateral area is

108 square units.

Explanation:

Answer 2

• slant height: 6 units
• lateral area: 108 square units

Explanation:

Given

A right regular hexagonal pyramid with ...

• base side length 6 units
• base apothem 3√3 units
• height 3 units

Find

• lateral face slant height
• pyramid lateral surface area

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.

__

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.