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.

slant height: 6 units lateral area: 108 square units

Step-by-step 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.

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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.