# Find the Surface Area pyramid (7cm)(25cm)(24cm) h=7cml=24cmw=25cm
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=24, the width w=25, and the height h=7 into the formula for surface area of a pyramid.
24⋅25+25⋅(242)2+(7)2+24⋅(252)2+(7)2
Simplify each term.
Multiply 24 by 25.
600+25⋅(242)2+(7)2+24⋅(252)2+(7)2
Divide 24 by 2.
600+25⋅122+(7)2+24⋅(252)2+(7)2
Raise 12 to the power of 2.
600+25⋅144+(7)2+24⋅(252)2+(7)2
Raise 7 to the power of 2.
600+25⋅144+49+24⋅(252)2+(7)2
Add 144 and 49.
600+25⋅193+24⋅(252)2+(7)2
Apply the product rule to 252.
600+25193+24⋅25222+(7)2
Raise 25 to the power of 2.
600+25193+24⋅62522+(7)2
Raise 2 to the power of 2.
600+25193+24⋅6254+(7)2
Raise 7 to the power of 2.
600+25193+24⋅6254+49
To write 49 as a fraction with a common denominator, multiply by 44.
600+25193+24⋅6254+49⋅44
Combine 49 and 44.
600+25193+24⋅6254+49⋅44
Combine the numerators over the common denominator.
600+25193+24⋅625+49⋅44
Simplify the numerator.
Multiply 49 by 4.
600+25193+24⋅625+1964
Add 625 and 196.
600+25193+24⋅8214
600+25193+24⋅8214
Rewrite 8214 as 8214.
600+25193+24⋅8214
Simplify the denominator.
Rewrite 4 as 22.
600+25193+24⋅82122
Pull terms out from under the radical, assuming positive real numbers.
600+25193+24⋅8212
600+25193+24⋅8212
Cancel the common factor of 2.
Factor 2 out of 24.
600+25193+2(12)⋅8212
Cancel the common factor.
600+25193+2⋅12⋅8212
Rewrite the expression.
600+25193+12⋅821
600+25193+12821
600+25193+12821
Calculate the approximate solution to 4 decimal places.
1291.1483(cm)2
Find the Surface Area pyramid (7cm)(25cm)(24cm)

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