Find the Surface Area pyramid (11)(3)(8)

Math
h=11l=8w=3
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=8, the width w=3, and the height h=11 into the formula for surface area of a pyramid.
8⋅3+3⋅(82)2+(11)2+8⋅(32)2+(11)2
Simplify each term.
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Multiply 8 by 3.
24+3⋅(82)2+(11)2+8⋅(32)2+(11)2
Divide 8 by 2.
24+3⋅42+(11)2+8⋅(32)2+(11)2
Raise 4 to the power of 2.
24+3⋅16+(11)2+8⋅(32)2+(11)2
Raise 11 to the power of 2.
24+3⋅16+121+8⋅(32)2+(11)2
Add 16 and 121.
24+3⋅137+8⋅(32)2+(11)2
Apply the product rule to 32.
24+3137+8⋅3222+(11)2
Raise 3 to the power of 2.
24+3137+8⋅922+(11)2
Raise 2 to the power of 2.
24+3137+8⋅94+(11)2
Raise 11 to the power of 2.
24+3137+8⋅94+121
To write 121 as a fraction with a common denominator, multiply by 44.
24+3137+8⋅94+121⋅44
Combine 121 and 44.
24+3137+8⋅94+121⋅44
Combine the numerators over the common denominator.
24+3137+8⋅9+121⋅44
Simplify the numerator.
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Multiply 121 by 4.
24+3137+8⋅9+4844
Add 9 and 484.
24+3137+8⋅4934
24+3137+8⋅4934
Rewrite 4934 as 4934.
24+3137+8⋅4934
Simplify the denominator.
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Rewrite 4 as 22.
24+3137+8⋅49322
Pull terms out from under the radical, assuming positive real numbers.
24+3137+8⋅4932
24+3137+8⋅4932
Cancel the common factor of 2.
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Factor 2 out of 8.
24+3137+2(4)⋅4932
Cancel the common factor.
24+3137+2⋅4⋅4932
Rewrite the expression.
24+3137+4⋅493
24+3137+4493
24+3137+4493
Calculate the approximate solution to 4 decimal places.
147.9285
Find the Surface Area pyramid (11)(3)(8)

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