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Stella [2.4K]
3 years ago
13

A parent died and left an estate to four children. One inherited

Mathematics
1 answer:
svetoff [14.1K]3 years ago
3 0
1-0.5-0.125-0.25= 1-0.875=0.125
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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 i
Setler79 [48]

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}

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