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

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)