Find the Surface Area pyramid (6)(9)(3)

Math
h=6l=3w=9
The surface area of a pyramid is equal to the sum of the areas of each side of the pyramid. The base of the pyramid has area lw, and sl and sw represent the slant height on the length and slant height on the width.
(length)⋅(width)+(width)⋅sl+(length)⋅sw
Substitute the values of the length l=3, the width w=9, and the height h=6 into the formula for surface area of a pyramid.
3⋅9+9⋅(32)2+(6)2+3⋅(92)2+(6)2
Simplify each term.
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Multiply 3 by 9.
27+9⋅(32)2+(6)2+3⋅(92)2+(6)2
Apply the product rule to 32.
27+9⋅3222+(6)2+3⋅(92)2+(6)2
Raise 3 to the power of 2.
27+9⋅922+(6)2+3⋅(92)2+(6)2
Raise 2 to the power of 2.
27+9⋅94+(6)2+3⋅(92)2+(6)2
Raise 6 to the power of 2.
27+9⋅94+36+3⋅(92)2+(6)2
To write 36 as a fraction with a common denominator, multiply by 44.
27+9⋅94+36⋅44+3⋅(92)2+(6)2
Combine 36 and 44.
27+9⋅94+36⋅44+3⋅(92)2+(6)2
Combine the numerators over the common denominator.
27+9⋅9+36⋅44+3⋅(92)2+(6)2
Simplify the numerator.
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Multiply 36 by 4.
27+9⋅9+1444+3⋅(92)2+(6)2
Add 9 and 144.
27+9⋅1534+3⋅(92)2+(6)2
27+9⋅1534+3⋅(92)2+(6)2
Rewrite 1534 as 1534.
27+9⋅1534+3⋅(92)2+(6)2
Simplify the numerator.
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Rewrite 153 as 32⋅17.
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Factor 9 out of 153.
27+9⋅9(17)4+3⋅(92)2+(6)2
Rewrite 9 as 32.
27+9⋅32⋅174+3⋅(92)2+(6)2
27+9⋅32⋅174+3⋅(92)2+(6)2
Pull terms out from under the radical.
27+9⋅3174+3⋅(92)2+(6)2
27+9⋅3174+3⋅(92)2+(6)2
Simplify the denominator.
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Rewrite 4 as 22.
27+9⋅31722+3⋅(92)2+(6)2
Pull terms out from under the radical, assuming positive real numbers.
27+9⋅3172+3⋅(92)2+(6)2
27+9⋅3172+3⋅(92)2+(6)2
Multiply 93172.
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Combine 9 and 3172.
27+9(317)2+3⋅(92)2+(6)2
Multiply 3 by 9.
27+27172+3⋅(92)2+(6)2
27+27172+3⋅(92)2+(6)2
Apply the product rule to 92.
27+27172+3⋅9222+(6)2
Raise 9 to the power of 2.
27+27172+3⋅8122+(6)2
Raise 2 to the power of 2.
27+27172+3⋅814+(6)2
Raise 6 to the power of 2.
27+27172+3⋅814+36
To write 36 as a fraction with a common denominator, multiply by 44.
27+27172+3⋅814+36⋅44
Combine 36 and 44.
27+27172+3⋅814+36⋅44
Combine the numerators over the common denominator.
27+27172+3⋅81+36⋅44
Simplify the numerator.
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Multiply 36 by 4.
27+27172+3⋅81+1444
Add 81 and 144.
27+27172+3⋅2254
27+27172+3⋅2254
Rewrite 2254 as 2254.
27+27172+3⋅2254
Simplify the numerator.
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Rewrite 225 as 152.
27+27172+3⋅1524
Pull terms out from under the radical, assuming positive real numbers.
27+27172+3⋅154
27+27172+3⋅154
Simplify the denominator.
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Rewrite 4 as 22.
27+27172+3⋅1522
Pull terms out from under the radical, assuming positive real numbers.
27+27172+3⋅152
27+27172+3⋅152
Multiply 3(152).
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Combine 3 and 152.
27+27172+3⋅152
Multiply 3 by 15.
27+27172+452
27+27172+452
27+27172+452
To write 27 as a fraction with a common denominator, multiply by 22.
27⋅22+452+27172
Combine 27 and 22.
27⋅22+452+27172
Combine the numerators over the common denominator.
27⋅2+452+27172
Simplify the numerator.
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Multiply 27 by 2.
54+452+27172
Add 54 and 45.
992+27172
992+27172
Calculate the approximate solution to 4 decimal places.
105.1619
Find the Surface Area pyramid (6)(9)(3)

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