Apyramid has a regular hexagonal base with the side lengths of 4 and a slant height of 6. find the total area of the pyramid..

113.57 unit²

Step-by-step explanation:

Surface area of a pyramid with regular hexagonal base

= Area of slant sides + area of Hexagonal base

Area of one slant side = (side of base) × slant height

                                    = × 6 × 4

                                    = 3 × 4

                                    = 12 unit²

Since hexagonal pyramid has 6 slant sides.

So area of sic slant sides = 6 × 12 = 72 unit²

Now for the area of hexagonal base we will take triangle ABC.

∠BAC = 60°    [angle formed at center = ]

and ∠CAD = 30°

Now tan 30° = =

AD =

Now hexagonal base area = 6 × [ (BC)(AD)]

6 × [ × ] =  

Therefore area of the pyramid = 72 + 41.57 = 113.57 unit²

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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70

step-by-step explanation:

2*5=10

4*15=60

60+10=

70