The surface area of a rectangular prism is found using the formula SA = 2(lw + lh + wh), where l is length, w is width, and h is height. If the surface area of a rectangular prism is 324km^2
, with length 5 m and width 12 m, what is the height, in meters?
To solve the given problem you first have to plug all the numbers in....
324 m² is the SA so 324 m² = 2[(5m × 12m) + (5m × h) + (12m × h)] You want to find the variable h so first start by dividing 342 by 2 which will make your equation simpler to solve.
= 162 m² = (5m × 12m) + (5m × h) + (12m × h)
Multiply your "lw" together 5m × 12m = 60m² and you have
162 m² = 60 m² + (5m × h) + (12m × h) You can subtract 162 m² by 60 m² leaving 102 m² = (5m × h) + (12m × h)
Then combine your like terms of h....5m × h + 12m × h = 17m × h so you now have
102m² = 17m × h and to get (h) by itself to solve for it you can then divide by 17 leaving 6m = (h) making your height equal 6 meters.
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(SA/2 - lw) = (h(l+w) ...... Subtract terms not containing (h) (SA/2 - lw) ÷ (l+w) = (h) ..... Divide by the coefficient of (h)
(324/2 - 5 × 12) ÷ (5+12) = (h) ... Plug in the numbers
