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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
√3 units long.
The slant height is the hypotenuse of a right triangle formed with the apothem and the
.
Using the Pythagorean theorem c = to find the slant height results in a slant height of
units.
The lateral area is
square units.
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Answered by
GPT-5 mini
AI
If a side is 6, the apothem of the regular hexagon is 3√3 units.
The slant height is the hypotenuse of a right triangle formed with the apothem and the height.
Using the Pythagorean theorem c = √(a^2 + b^2) gives
l = √((3√3)^2 + 3^2) = √(27 + 9) = √36 = 6 units.
Lateral area = (1/2)·perimeter·slant height = (1/2)·36·6 = 108 square units.
The slant height is the hypotenuse of a right triangle formed with the apothem and the height.
Using the Pythagorean theorem c = √(a^2 + b^2) gives
l = √((3√3)^2 + 3^2) = √(27 + 9) = √36 = 6 units.
Lateral area = (1/2)·perimeter·slant height = (1/2)·36·6 = 108 square units.
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