# Find the Surface Area pyramid (11)(5)(17) h=11l=17w=5
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=17, the width w=5, and the height h=11 into the formula for surface area of a pyramid.
17⋅5+5⋅(172)2+(11)2+17⋅(52)2+(11)2
Simplify each term.
Multiply 17 by 5.
85+5⋅(172)2+(11)2+17⋅(52)2+(11)2
Apply the product rule to 172.
85+5⋅17222+(11)2+17⋅(52)2+(11)2
Raise 17 to the power of 2.
85+5⋅28922+(11)2+17⋅(52)2+(11)2
Raise 2 to the power of 2.
85+5⋅2894+(11)2+17⋅(52)2+(11)2
Raise 11 to the power of 2.
85+5⋅2894+121+17⋅(52)2+(11)2
To write 121 as a fraction with a common denominator, multiply by 44.
85+5⋅2894+121⋅44+17⋅(52)2+(11)2
Combine 121 and 44.
85+5⋅2894+121⋅44+17⋅(52)2+(11)2
Combine the numerators over the common denominator.
85+5⋅289+121⋅44+17⋅(52)2+(11)2
Simplify the numerator.
Multiply 121 by 4.
85+5⋅289+4844+17⋅(52)2+(11)2
Add 289 and 484.
85+5⋅7734+17⋅(52)2+(11)2
85+5⋅7734+17⋅(52)2+(11)2
Rewrite 7734 as 7734.
85+5⋅7734+17⋅(52)2+(11)2
Simplify the denominator.
Rewrite 4 as 22.
85+5⋅77322+17⋅(52)2+(11)2
Pull terms out from under the radical, assuming positive real numbers.
85+5⋅7732+17⋅(52)2+(11)2
85+57732+17⋅(52)2+(11)2
Apply the product rule to 52.
85+57732+17⋅5222+(11)2
Raise 5 to the power of 2.
85+57732+17⋅2522+(11)2
Raise 2 to the power of 2.
85+57732+17⋅254+(11)2
Raise 11 to the power of 2.
85+57732+17⋅254+121
To write 121 as a fraction with a common denominator, multiply by 44.
85+57732+17⋅254+121⋅44
Combine 121 and 44.
85+57732+17⋅254+121⋅44
Combine the numerators over the common denominator.
85+57732+17⋅25+121⋅44
Simplify the numerator.
Multiply 121 by 4.
85+57732+17⋅25+4844
Add 25 and 484.
85+57732+17⋅5094
85+57732+17⋅5094
Rewrite 5094 as 5094.
85+57732+17⋅5094
Simplify the denominator.
Rewrite 4 as 22.
85+57732+17⋅50922
Pull terms out from under the radical, assuming positive real numbers.
85+57732+17⋅5092
85+57732+175092
85+57732+175092
Calculate the approximate solution to 4 decimal places.
346.2759
Find the Surface Area pyramid (11)(5)(17)

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