# Find the Surface Area pyramid (10)(9)(6) h=10l=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=10 into the formula for surface area of a pyramid.
6⋅9+9⋅(62)2+(10)2+6⋅(92)2+(10)2
Simplify each term.
Multiply 6 by 9.
54+9⋅(62)2+(10)2+6⋅(92)2+(10)2
Divide 6 by 2.
54+9⋅32+(10)2+6⋅(92)2+(10)2
Raise 3 to the power of 2.
54+9⋅9+(10)2+6⋅(92)2+(10)2
Raise 10 to the power of 2.
54+9⋅9+100+6⋅(92)2+(10)2
Add 9 and 100.
54+9⋅109+6⋅(92)2+(10)2
Apply the product rule to 92.
54+9109+6⋅9222+(10)2
Raise 9 to the power of 2.
54+9109+6⋅8122+(10)2
Raise 2 to the power of 2.
54+9109+6⋅814+(10)2
Raise 10 to the power of 2.
54+9109+6⋅814+100
To write 100 as a fraction with a common denominator, multiply by 44.
54+9109+6⋅814+100⋅44
Combine 100 and 44.
54+9109+6⋅814+100⋅44
Combine the numerators over the common denominator.
54+9109+6⋅81+100⋅44
Simplify the numerator.
Multiply 100 by 4.
54+9109+6⋅81+4004
Add 81 and 400.
54+9109+6⋅4814
54+9109+6⋅4814
Rewrite 4814 as 4814.
54+9109+6⋅4814
Simplify the denominator.
Rewrite 4 as 22.
54+9109+6⋅48122
Pull terms out from under the radical, assuming positive real numbers.
54+9109+6⋅4812
54+9109+6⋅4812
Cancel the common factor of 2.
Factor 2 out of 6.
54+9109+2(3)⋅4812
Cancel the common factor.
54+9109+2⋅3⋅4812
Rewrite the expression.
54+9109+3⋅481
54+9109+3481
54+9109+3481
Calculate the approximate solution to 4 decimal places.
213.7579
Find the Surface Area pyramid (10)(9)(6)

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