# Find the Surface Area pyramid (8)(8.1)(7) h=8l=7w=8.1
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=7, the width w=8.1, and the height h=8 into the formula for surface area of a pyramid.
7⋅8.1+8.1⋅(72)2+(8)2+7⋅(8.12)2+(8)2
Simplify each term.
Multiply 7 by 8.1.
56.7+8.1⋅(72)2+(8)2+7⋅(8.12)2+(8)2
Apply the product rule to 72.
56.7+8.1⋅7222+(8)2+7⋅(8.12)2+(8)2
Raise 7 to the power of 2.
56.7+8.1⋅4922+(8)2+7⋅(8.12)2+(8)2
Raise 2 to the power of 2.
56.7+8.1⋅494+(8)2+7⋅(8.12)2+(8)2
Raise 8 to the power of 2.
56.7+8.1⋅494+64+7⋅(8.12)2+(8)2
To write 64 as a fraction with a common denominator, multiply by 44.
56.7+8.1⋅494+64⋅44+7⋅(8.12)2+(8)2
Combine 64 and 44.
56.7+8.1⋅494+64⋅44+7⋅(8.12)2+(8)2
Combine the numerators over the common denominator.
56.7+8.1⋅49+64⋅44+7⋅(8.12)2+(8)2
Simplify the numerator.
Multiply 64 by 4.
56.7+8.1⋅49+2564+7⋅(8.12)2+(8)2
Add 49 and 256.
56.7+8.1⋅3054+7⋅(8.12)2+(8)2
56.7+8.1⋅3054+7⋅(8.12)2+(8)2
Rewrite 3054 as 3054.
56.7+8.1⋅3054+7⋅(8.12)2+(8)2
Simplify the denominator.
Rewrite 4 as 22.
56.7+8.1⋅30522+7⋅(8.12)2+(8)2
Pull terms out from under the radical, assuming positive real numbers.
56.7+8.1⋅3052+7⋅(8.12)2+(8)2
56.7+8.1⋅3052+7⋅(8.12)2+(8)2
Cancel the common factor of 2.
Factor 2 out of 8.1.
56.7+2(4.05)⋅3052+7⋅(8.12)2+(8)2
Cancel the common factor.
56.7+2⋅4.05⋅3052+7⋅(8.12)2+(8)2
Rewrite the expression.
56.7+4.05⋅305+7⋅(8.12)2+(8)2
56.7+4.05⋅305+7⋅(8.12)2+(8)2
Multiply 4.05 by 305.
56.7+70.73020924+7⋅(8.12)2+(8)2
Divide 8.1 by 2.
56.7+70.73020924+7⋅4.052+(8)2
Raise 4.05 to the power of 2.
56.7+70.73020924+7⋅16.4025+(8)2
Raise 8 to the power of 2.
56.7+70.73020924+7⋅16.4025+64
Add 16.4025 and 64.
56.7+70.73020924+780.4025
56.7+70.73020924+780.4025
Simplify by adding terms.
Add 56.7 and 70.73020924.
127.43020924+780.4025
Add 127.43020924 and 780.4025.
190.19741804
190.19741804
Calculate the approximate solution to 4 decimal places.
190.1974
Find the Surface Area pyramid (8)(8.1)(7)

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