h=6ml=10mw=x

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=10, the width w=x, and the height h=6 into the formula for surface area of a pyramid.

10⋅x+x⋅(102)2+(6)2+10⋅(x2)2+(6)2

Divide 10 by 2.

10x+x⋅52+(6)2+10⋅(x2)2+(6)2

Raise 5 to the power of 2.

10x+x⋅25+(6)2+10⋅(x2)2+(6)2

Raise 6 to the power of 2.

10x+x⋅25+36+10⋅(x2)2+(6)2

Add 25 and 36.

10x+x⋅61+10⋅(x2)2+(6)2

Apply the product rule to x2.

10x+x61+10⋅x222+(6)2

Raise 2 to the power of 2.

10x+x61+10⋅x24+(6)2

Raise 6 to the power of 2.

10x+x61+10⋅x24+36

To write 36 as a fraction with a common denominator, multiply by 44.

10x+x61+10⋅x24+36⋅44

Combine 36 and 44.

10x+x61+10⋅x24+36⋅44

Combine the numerators over the common denominator.

10x+x61+10⋅x2+36⋅44

Multiply 36 by 4.

10x+x61+10⋅x2+1444

Rewrite x2+1444 as (12)2(x2+144).

Factor the perfect power 12 out of x2+144.

10x+x61+10⋅12(x2+144)4

Factor the perfect power 22 out of 4.

10x+x61+10⋅12(x2+144)22⋅1

Rearrange the fraction 12(x2+144)22⋅1.

10x+x61+10⋅(12)2(x2+144)

10x+x61+10⋅(12)2(x2+144)

Pull terms out from under the radical.

10x+x61+10⋅(12×2+144)

Combine 12 and x2+144.

10x+x61+10⋅x2+1442

Cancel the common factor of 2.

Factor 2 out of 10.

10x+x61+2(5)⋅x2+1442

Cancel the common factor.

10x+x61+2⋅5⋅x2+1442

Rewrite the expression.

10x+x61+5⋅x2+144

10x+x61+5×2+144

10x+x61+5×2+144m2

Find the Surface Area pyramid (6m)(x)(10m)