Question

representing area with a polynomial expression
find a simplified expression to represent the area of the triangle. the area formula for a triangle is \\( \frac { 1 } { 2 } b h \\), where \\( b \\) is the base and \\( h \\) is the height.
the expression that represents the area of this triangle is \\( \square x ^ { 2 } + \square x + \square \mathrm { cm } ^ { 2 } \\).

Explanation:

Step1: Substitute base and height into formula

The base \( b=(4x - 2)\) and height \( h=(2x + 12)\). Using \(A=\frac{1}{2}bh\), we get \(A=\frac{1}{2}(4x - 2)(2x + 12)\).

Step2: Simplify \((4x - 2)(2x + 12)\)

Use the FOIL method: \((4x\times2x)+(4x\times12)+(- 2\times2x)+(-2\times12)=8x^{2}+48x-4x - 24=8x^{2}+44x - 24\).

Step3: Multiply by \(\frac{1}{2}\)

\(A=\frac{1}{2}(8x^{2}+44x - 24)=4x^{2}+22x - 12\).

Answer:

\(4x^{2}+22x - 12\)