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Anastasy [175]
3 years ago
9

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 i

s 3 units long The slant height is the hypotenuse of a right triangle formed with the apothem and the Using the Pythagorean theorem c- + b2 to find the slant height results in a slant height of units The lateral area issquare units
Mathematics
2 answers:
Setler79 [48]3 years ago
3 0

Answer:

Part a) The slant height is 3\sqrt{2}\ units

Part b) The lateral area is equal to 54\sqrt{2}\ units^{2}

Step-by-step explanation:

we know that

The lateral area of a right pyramid with a regular hexagon base is equal to the area of its six triangular faces

so

LA=6[\frac{1}{2}(b)(l)]

where

b is the length side of the hexagon

l is the slant height of the pyramid

Part a) Find the slant height l

Applying the Pythagoras Theorem

l^{2}=h^{2} +a^{2}

where

h is the height of the pyramid

a is the apothem

we have

h=3\ units

a=3\ units

substitute

l^{2}=3^{2} +3^{2}

l^{2}=18

l=3\sqrt{2}\ units

Part b) Find the lateral area

LA=6[\frac{1}{2}(b)(l)]

we have

b=6\ units

l=3\sqrt{2}\ units

substitute the values

LA=6[\frac{1}{2}(6)(3\sqrt{2})]=54\sqrt{2}\ units^{2}

djverab [1.8K]3 years ago
3 0

Answer:

3

height of the pyramid

6

108

Step-by-step explanation:

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