Find the Surface Area pyramid (7.5)(9)(6)

Math
h=7.5l=6w=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=6, the width w=9, and the height h=7.5 into the formula for surface area of a pyramid.
6⋅9+9⋅(62)2+(7.5)2+6⋅(92)2+(7.5)2
Simplify each term.
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Multiply 6 by 9.
54+9⋅(62)2+(7.5)2+6⋅(92)2+(7.5)2
Divide 6 by 2.
54+9⋅32+(7.5)2+6⋅(92)2+(7.5)2
Raise 3 to the power of 2.
54+9⋅9+(7.5)2+6⋅(92)2+(7.5)2
Raise 7.5 to the power of 2.
54+9⋅9+56.25+6⋅(92)2+(7.5)2
Add 9 and 56.25.
54+9⋅65.25+6⋅(92)2+(7.5)2
Apply the product rule to 92.
54+965.25+6⋅9222+(7.5)2
Raise 9 to the power of 2.
54+965.25+6⋅8122+(7.5)2
Raise 2 to the power of 2.
54+965.25+6⋅814+(7.5)2
Raise 7.5 to the power of 2.
54+965.25+6⋅814+56.25
To write 56.25 as a fraction with a common denominator, multiply by 44.
54+965.25+6⋅814+56.25⋅44
Combine 56.25 and 44.
54+965.25+6⋅814+56.25⋅44
Combine the numerators over the common denominator.
54+965.25+6⋅81+56.25⋅44
Simplify the numerator.
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Multiply 56.25 by 4.
54+965.25+6⋅81+2254
Add 81 and 225.
54+965.25+6⋅3064
54+965.25+6⋅3064
Cancel the common factor of 306 and 4.
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Factor 2 out of 306.
54+965.25+6⋅2(153)4
Cancel the common factors.
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Factor 2 out of 4.
54+965.25+6⋅2⋅1532⋅2
Cancel the common factor.
54+965.25+6⋅2⋅1532⋅2
Rewrite the expression.
54+965.25+6⋅1532
54+965.25+6⋅1532
54+965.25+6⋅1532
Rewrite 1532 as 1532.
54+965.25+6⋅1532
Simplify the numerator.
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Rewrite 153 as 32⋅17.
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Factor 9 out of 153.
54+965.25+6⋅9(17)2
Rewrite 9 as 32.
54+965.25+6⋅32⋅172
54+965.25+6⋅32⋅172
Pull terms out from under the radical.
54+965.25+6⋅3172
54+965.25+6⋅3172
Multiply 3172 by 22.
54+965.25+6⋅(3172⋅22)
Combine and simplify the denominator.
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Multiply 3172 and 22.
54+965.25+6⋅317222
Raise 2 to the power of 1.
54+965.25+6⋅3172212
Raise 2 to the power of 1.
54+965.25+6⋅31722121
Use the power rule aman=am+n to combine exponents.
54+965.25+6⋅317221+1
Add 1 and 1.
54+965.25+6⋅317222
Rewrite 22 as 2.
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Use axn=axn to rewrite 2 as 212.
54+965.25+6⋅3172(212)2
Apply the power rule and multiply exponents, (am)n=amn.
54+965.25+6⋅3172212⋅2
Combine 12 and 2.
54+965.25+6⋅3172222
Cancel the common factor of 2.
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Cancel the common factor.
54+965.25+6⋅3172222
Divide 1 by 1.
54+965.25+6⋅317221
54+965.25+6⋅317221
Evaluate the exponent.
54+965.25+6⋅31722
54+965.25+6⋅31722
54+965.25+6⋅31722
Simplify the numerator.
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Combine using the product rule for radicals.
54+965.25+6⋅32⋅172
Multiply 2 by 17.
54+965.25+6⋅3342
54+965.25+6⋅3342
Cancel the common factor of 2.
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Factor 2 out of 6.
54+965.25+2(3)⋅3342
Cancel the common factor.
54+965.25+2⋅3⋅3342
Rewrite the expression.
54+965.25+3⋅(334)
54+965.25+3⋅(334)
Multiply 3 by 3.
54+965.25+934
54+965.25+934
Calculate the approximate solution to 4 decimal places.
179.1783
Find the Surface Area pyramid (7.5)(9)(6)

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