Question

1. the area of a trapezoid is found by using the formula $a = \frac{1}{2}h(b_1 + b_2)$. image of trapezoid with top base $5x - 4$, height $h = 6$, bottom base $3x + 10$ what expression represents the area of the trapezoid shown? \\(\bigcirc\\) a. $4x + 3$ \\(\bigcirc\\) b. $8x + 6$ \\(\bigcirc\\) c. $24x + 18$ \\(\bigcirc\\) d. $48x + 36$

Explanation:

Step1: Identify values for formula

We know the trapezoid area formula is \( A=\frac{1}{2}h(b_1 + b_2) \). Here, \( h = 6 \), \( b_1=5x - 4 \), and \( b_2 = 3x+10 \).

Step2: Substitute values into formula

Substitute the values into the formula: \( A=\frac{1}{2}\times6\times((5x - 4)+(3x + 10)) \). First, simplify the sum of the bases: \( (5x - 4)+(3x + 10)=8x + 6 \).

Step3: Simplify the expression

Now, multiply by \( \frac{1}{2}\times6 \). \( \frac{1}{2}\times6 = 3 \), so we have \( 3\times(8x + 6) \). Distribute the 3: \( 3\times8x+3\times6 = 24x+18 \).

Answer:

C. \( 24x + 18 \)