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What expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign?


A square shaped traffic sign is shown with length of one side labeled as 4x + 3.

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Below are the choices based on the question above:

16x2 + 12x + 9

  16x2 + 24x + 9

  8x2 + 9

  8x2 + 6

The answer is the second one 16x^2 +24x+9

JeanaShupp

Answer: \(\text{Area of the square shaped traffic sign }=16x^2+9+24x\)

Step-by-step explanation:

Given: The side of the square shaped traffic sign = 4x+3

We know that the area of square is given by:-

\(Area= side^2\)

Therefore, the area of the side of the square shaped field is given by:-

\(Area=(4x+3)^2\)

We know that , \((a+b)^2=a^2+b^2+2ab\)

Therefore,

\((4x+3)^2=(4x)^2+(3)^2+2(4x)(3)\\=16x^2+9+24x\)

Hence, \(\text{Area of the square shaped traffic sign }=16x^2+9+24x\)

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