Question

the area of a triangle is always one half the base b times the height h. if the base is represented by the expression 4x + 2 and the height is represented by 3x, which expression gives the area of the triangle? 9x 9x² 12x² + 6x 6x²+ 3x

Explanation:

Step1: Recall the area formula for a triangle

The formula for the area \( A \) of a triangle is \( A=\frac{1}{2}bh \), where \( b \) is the base and \( h \) is the height.

Step2: Substitute the given expressions for \( b \) and \( h \)

We are given that \( b = 4x + 2 \) and \( h=3x \). Substitute these into the formula:
\( A=\frac{1}{2}(4x + 2)(3x) \)

Step3: Distribute the multiplication

First, multiply \( \frac{1}{2} \) with \( (4x + 2) \):
\( \frac{1}{2}(4x+2)=2x + 1 \)
Then, multiply the result by \( 3x \):
\( (2x + 1)(3x)=2x\times3x+1\times3x = 6x^{2}+3x \)

Answer:

\( 6x^{2}+3x \) (corresponding to the option with this expression)