h=11l=9w=8

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=9, the width w=8, and the height h=11 into the formula for surface area of a pyramid.

9⋅8+8⋅(92)2+(11)2+9⋅(82)2+(11)2

Multiply 9 by 8.

72+8⋅(92)2+(11)2+9⋅(82)2+(11)2

Apply the product rule to 92.

72+8⋅9222+(11)2+9⋅(82)2+(11)2

Raise 9 to the power of 2.

72+8⋅8122+(11)2+9⋅(82)2+(11)2

Raise 2 to the power of 2.

72+8⋅814+(11)2+9⋅(82)2+(11)2

Raise 11 to the power of 2.

72+8⋅814+121+9⋅(82)2+(11)2

To write 121 as a fraction with a common denominator, multiply by 44.

72+8⋅814+121⋅44+9⋅(82)2+(11)2

Combine 121 and 44.

72+8⋅814+121⋅44+9⋅(82)2+(11)2

Combine the numerators over the common denominator.

72+8⋅81+121⋅44+9⋅(82)2+(11)2

Simplify the numerator.

Multiply 121 by 4.

72+8⋅81+4844+9⋅(82)2+(11)2

Add 81 and 484.

72+8⋅5654+9⋅(82)2+(11)2

72+8⋅5654+9⋅(82)2+(11)2

Rewrite 5654 as 5654.

72+8⋅5654+9⋅(82)2+(11)2

Simplify the denominator.

Rewrite 4 as 22.

72+8⋅56522+9⋅(82)2+(11)2

Pull terms out from under the radical, assuming positive real numbers.

72+8⋅5652+9⋅(82)2+(11)2

72+8⋅5652+9⋅(82)2+(11)2

Cancel the common factor of 2.

Factor 2 out of 8.

72+2(4)⋅5652+9⋅(82)2+(11)2

Cancel the common factor.

72+2⋅4⋅5652+9⋅(82)2+(11)2

Rewrite the expression.

72+4⋅565+9⋅(82)2+(11)2

72+4⋅565+9⋅(82)2+(11)2

Divide 8 by 2.

72+4565+9⋅42+(11)2

Raise 4 to the power of 2.

72+4565+9⋅16+(11)2

Raise 11 to the power of 2.

72+4565+9⋅16+121

Add 16 and 121.

72+4565+9137

72+4565+9137

Calculate the approximate solution to 4 decimal places.

272.4212

Find the Surface Area pyramid (11)(8)(9)