sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should notice that you may find the area of shaded region subtracting from the area of large right angle triangle, the area of small right angle triangle.

You need to evaluate the area of large right angle triangle considering the legs x+4 and x+6 such that:

`A = ((x+4)(x+6))/2`

You need to evaluate the area of small right angle triangle such that:

`a = ((x+4)(x-4))/2`

You may now evaluate the area of shaded region, hence, you need to subtract a from A such that:

`A - a = ((x+4)(x+6))/2 - ((x+4)(x-4))/2 `

Notice that you may factor out `(x+4)/2`  such that:

`A - a = (x+4)/2*(x + 6 - x + 4)`

`A - a = (x+4)/2*(10)`

`A - a = 5(x+4)`

You need to evaluate the area of shaded region for x = 12 in such that:

`A - a = 5(12+4) =gt A - a = 80 ` in^2

Hence, evaluating the area of shaded region in terms of x yields `A - a = 5(x+4)`  and evaluating the area if `x = 12`  in yields `A - a = 80 .` in^2

Sources:

klmd | Student | (Level 2) eNoter

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if you multiply everything out you will end up with this expression