Basic Math Examples

Find the Surface Area pyramid (6km)(6km)(8km)
h=6kml=8kmw=6kmh=6kml=8kmw=6km
Step 1
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 lwlw, and slsl and swsw represent the slant height on the length and slant height on the width.
(length)(width)+(width)sl+(length)sw(length)(width)+(width)sl+(length)sw
Step 2
Substitute the values of the length l=8l=8, the width w=6w=6, and the height h=6h=6 into the formula for surface area of a pyramid.
86+6(82)2+(6)2+8(62)2+(6)286+6(82)2+(6)2+8(62)2+(6)2
Step 3
Simplify each term.
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Step 3.1
Multiply 88 by 66.
48+6(82)2+(6)2+8(62)2+(6)248+6(82)2+(6)2+8(62)2+(6)2
Step 3.2
Divide 88 by 22.
48+642+(6)2+8(62)2+(6)248+642+(6)2+8(62)2+(6)2
Step 3.3
Raise 44 to the power of 22.
48+616+(6)2+8(62)2+(6)248+616+(6)2+8(62)2+(6)2
Step 3.4
Raise 66 to the power of 22.
48+616+36+8(62)2+(6)248+616+36+8(62)2+(6)2
Step 3.5
Add 1616 and 3636.
48+652+8(62)2+(6)248+652+8(62)2+(6)2
Step 3.6
Rewrite 5252 as 22132213.
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Step 3.6.1
Factor 44 out of 5252.
48+64(13)+8(62)2+(6)248+64(13)+8(62)2+(6)2
Step 3.6.2
Rewrite 44 as 2222.
48+62213+8(62)2+(6)248+62213+8(62)2+(6)2
48+62213+8(62)2+(6)248+62213+8(62)2+(6)2
Step 3.7
Pull terms out from under the radical.
48+6(213)+8(62)2+(6)248+6(213)+8(62)2+(6)2
Step 3.8
Multiply 22 by 66.
48+1213+8(62)2+(6)248+1213+8(62)2+(6)2
Step 3.9
Divide 66 by 22.
48+1213+832+(6)248+1213+832+(6)2
Step 3.10
Raise 33 to the power of 22.
48+1213+89+(6)248+1213+89+(6)2
Step 3.11
Raise 66 to the power of 22.
48+1213+89+3648+1213+89+36
Step 3.12
Add 99 and 3636.
48+1213+84548+1213+845
Step 3.13
Rewrite 4545 as 325325.
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Step 3.13.1
Factor 99 out of 4545.
48+1213+89(5)48+1213+89(5)
Step 3.13.2
Rewrite 99 as 3232.
48+1213+832548+1213+8325
48+1213+832548+1213+8325
Step 3.14
Pull terms out from under the radical.
48+1213+8(35)48+1213+8(35)
Step 3.15
Multiply 33 by 88.
48+1213+24548+1213+245
48+1213+24548+1213+245
Step 4
Calculate the approximate solution to 44 decimal places.
144.9322(km)2144.9322(km)2
 [x2  12  π  xdx ]  x2  12  π  xdx