SOLUTION: Area of a parallelogram Find a trinomial A(x) that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x + 3 meters. Find A(3).

Algebra ->  Parallelograms -> SOLUTION: Area of a parallelogram Find a trinomial A(x) that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x + 3 meters. Find A(3).      Log On


   

Question 199777: Area of a parallelogram
Find a trinomial A(x) that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x + 3 meters. Find A(3).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Area of a parallelogram:

Area = Base * Height ----> A = bh


A=bh Start with the given equation.


A=%283x%2B2%29%282x%2B3%29 Plug in b=3x%2B2 and h=2x%2B3 (the given base and height)


A=%283x%29%282x%29%2B%283x%29%283%29%2B%282%29%282x%29%2B%282%29%283%29 FOIL


A=6x%5E2%2B9x%2B4x%2B6 Multiply


A=6x%5E2%2B13x%2B6 Combine like terms.


So the trinomial for the area is A%28x%29=6x%5E2%2B13x%2B6


Now let's find A(3).


A%28x%29=6x%5E2%2B13x%2B6 Start with the given equation.


A%283%29=6%283%29%5E2%2B13%283%29%2B6 Plug in x=3.


A%283%29=6%289%29%2B13%283%29%2B6 Square 3 to get 9.


A%283%29=54%2B13%283%29%2B6 Multiply 6 and 9 to get 54.


A%283%29=54%2B39%2B6 Multiply 13 and 3 to get 39.


A%283%29=99 Combine like terms.


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