# Find the Surface Area pyramid (10m)(10m)(12m) h=10ml=12mw=10m
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=12, the width w=10, and the height h=10 into the formula for surface area of a pyramid.
12⋅10+10⋅(122)2+(10)2+12⋅(102)2+(10)2
Simplify each term.
Multiply 12 by 10.
120+10⋅(122)2+(10)2+12⋅(102)2+(10)2
Divide 12 by 2.
120+10⋅62+(10)2+12⋅(102)2+(10)2
Raise 6 to the power of 2.
120+10⋅36+(10)2+12⋅(102)2+(10)2
Raise 10 to the power of 2.
120+10⋅36+100+12⋅(102)2+(10)2
Add 36 and 100.
120+10⋅136+12⋅(102)2+(10)2
Rewrite 136 as 22⋅34.
Factor 4 out of 136.
120+10⋅4(34)+12⋅(102)2+(10)2
Rewrite 4 as 22.
120+10⋅22⋅34+12⋅(102)2+(10)2
120+10⋅22⋅34+12⋅(102)2+(10)2
Pull terms out from under the radical.
120+10⋅(234)+12⋅(102)2+(10)2
Multiply 2 by 10.
120+2034+12⋅(102)2+(10)2
Divide 10 by 2.
120+2034+12⋅52+(10)2
Raise 5 to the power of 2.
120+2034+12⋅25+(10)2
Raise 10 to the power of 2.
120+2034+12⋅25+100
Add 25 and 100.
120+2034+12⋅125
Rewrite 125 as 52⋅5.
Factor 25 out of 125.
120+2034+12⋅25(5)
Rewrite 25 as 52.
120+2034+12⋅52⋅5
120+2034+12⋅52⋅5
Pull terms out from under the radical.
120+2034+12⋅(55)
Multiply 5 by 12.
120+2034+605
120+2034+605
Calculate the approximate solution to 4 decimal places.
370.7831m2
Find the Surface Area pyramid (10m)(10m)(12m)

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