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A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
T. A.=

Step-by-step explanation:

(3a2-b)(3a2+b) are the factor

72 + 36 square root 3

Step-by-step explanation:

equation for whole thing : LA + area of base

first need to find lateral area = sum of all lateral faces

to find 1 lateral face (1/2)(slant height)(side)

Given both (1/2)(6)(4) = 12

do times 6 = 12 times 6 = 72  

that is your lateral area

Now need to fine area of hexagon

area of polygon = (1/2)( apothem)(perimeter)

perimeter = 4 times 6 = 24

For apothem need to find other sides of half triangle in midle which is a 30-60-90 triangle so short leg = 1/2 hypotenuse which given so 1/2 6 = 3

long leg = short times square root of 3 = 3 square root 3

that is apothom  so (1/2)(3 square root 3)(24)= 36 square root 3

Put together to get 72 + 36 square root 3