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3 years ago

Luguin

Mathematics

1 answer:

SVETLANKA909090 [29]3 years ago

7 0

Answer:

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.

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.

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