Find the Surface Area pyramid (11)(11)(11)

Math
h=11l=11w=11
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=11, the width w=11, and the height h=11 into the formula for surface area of a pyramid.
11⋅11+11⋅(112)2+(11)2+11⋅(112)2+(11)2
Simplify each term.
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Multiply 11 by 11.
121+11⋅(112)2+(11)2+11⋅(112)2+(11)2
Apply the product rule to 112.
121+11⋅11222+(11)2+11⋅(112)2+(11)2
Raise 11 to the power of 2.
121+11⋅12122+(11)2+11⋅(112)2+(11)2
Raise 2 to the power of 2.
121+11⋅1214+(11)2+11⋅(112)2+(11)2
Raise 11 to the power of 2.
121+11⋅1214+121+11⋅(112)2+(11)2
To write 121 as a fraction with a common denominator, multiply by 44.
121+11⋅1214+121⋅44+11⋅(112)2+(11)2
Combine 121 and 44.
121+11⋅1214+121⋅44+11⋅(112)2+(11)2
Combine the numerators over the common denominator.
121+11⋅121+121⋅44+11⋅(112)2+(11)2
Simplify the numerator.
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Multiply 121 by 4.
121+11⋅121+4844+11⋅(112)2+(11)2
Add 121 and 484.
121+11⋅6054+11⋅(112)2+(11)2
121+11⋅6054+11⋅(112)2+(11)2
Rewrite 6054 as 6054.
121+11⋅6054+11⋅(112)2+(11)2
Simplify the numerator.
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Rewrite 605 as 112⋅5.
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Factor 121 out of 605.
121+11⋅121(5)4+11⋅(112)2+(11)2
Rewrite 121 as 112.
121+11⋅112⋅54+11⋅(112)2+(11)2
121+11⋅112⋅54+11⋅(112)2+(11)2
Pull terms out from under the radical.
121+11⋅1154+11⋅(112)2+(11)2
121+11⋅1154+11⋅(112)2+(11)2
Simplify the denominator.
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Rewrite 4 as 22.
121+11⋅11522+11⋅(112)2+(11)2
Pull terms out from under the radical, assuming positive real numbers.
121+11⋅1152+11⋅(112)2+(11)2
121+11⋅1152+11⋅(112)2+(11)2
Multiply 111152.
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Combine 11 and 1152.
121+11(115)2+11⋅(112)2+(11)2
Multiply 11 by 11.
121+12152+11⋅(112)2+(11)2
121+12152+11⋅(112)2+(11)2
Apply the product rule to 112.
121+12152+11⋅11222+(11)2
Raise 11 to the power of 2.
121+12152+11⋅12122+(11)2
Raise 2 to the power of 2.
121+12152+11⋅1214+(11)2
Raise 11 to the power of 2.
121+12152+11⋅1214+121
To write 121 as a fraction with a common denominator, multiply by 44.
121+12152+11⋅1214+121⋅44
Combine 121 and 44.
121+12152+11⋅1214+121⋅44
Combine the numerators over the common denominator.
121+12152+11⋅121+121⋅44
Simplify the numerator.
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Multiply 121 by 4.
121+12152+11⋅121+4844
Add 121 and 484.
121+12152+11⋅6054
121+12152+11⋅6054
Rewrite 6054 as 6054.
121+12152+11⋅6054
Simplify the numerator.
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Rewrite 605 as 112⋅5.
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Factor 121 out of 605.
121+12152+11⋅121(5)4
Rewrite 121 as 112.
121+12152+11⋅112⋅54
121+12152+11⋅112⋅54
Pull terms out from under the radical.
121+12152+11⋅1154
121+12152+11⋅1154
Simplify the denominator.
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Rewrite 4 as 22.
121+12152+11⋅11522
Pull terms out from under the radical, assuming positive real numbers.
121+12152+11⋅1152
121+12152+11⋅1152
Multiply 111152.
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Combine 11 and 1152.
121+12152+11(115)2
Multiply 11 by 11.
121+12152+12152
121+12152+12152
121+12152+12152
Simplify terms.
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Combine fractions with similar denominators.
121+1215+12152
Add 1215 and 1215.
121+24252
Cancel the common factor of 242 and 2.
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Factor 2 out of 2425.
121+2(1215)2
Cancel the common factors.
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Factor 2 out of 2.
121+2(1215)2(1)
Cancel the common factor.
121+2(1215)2⋅1
Rewrite the expression.
121+12151
Divide 1215 by 1.
121+1215
121+1215
121+1215
121+1215
Calculate the approximate solution to 4 decimal places.
391.5642
Find the Surface Area pyramid (11)(11)(11)

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