h=4l=10w=12

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=12, and the height h=4 into the formula for surface area of a pyramid.

10⋅12+12⋅(102)2+(4)2+10⋅(122)2+(4)2

Multiply 10 by 12.

120+12⋅(102)2+(4)2+10⋅(122)2+(4)2

Divide 10 by 2.

120+12⋅52+(4)2+10⋅(122)2+(4)2

Raise 5 to the power of 2.

120+12⋅25+(4)2+10⋅(122)2+(4)2

Raise 4 to the power of 2.

120+12⋅25+16+10⋅(122)2+(4)2

Add 25 and 16.

120+12⋅41+10⋅(122)2+(4)2

Divide 12 by 2.

120+1241+10⋅62+(4)2

Raise 6 to the power of 2.

120+1241+10⋅36+(4)2

Raise 4 to the power of 2.

120+1241+10⋅36+16

Add 36 and 16.

120+1241+10⋅52

Rewrite 52 as 22⋅13.

Factor 4 out of 52.

120+1241+10⋅4(13)

Rewrite 4 as 22.

120+1241+10⋅22⋅13

120+1241+10⋅22⋅13

Pull terms out from under the radical.

120+1241+10⋅(213)

Multiply 2 by 10.

120+1241+2013

120+1241+2013

Calculate the approximate solution to 4 decimal places.

268.9485

Find the Surface Area pyramid (4)(12)(10)