Question

represents the missin dimension x. the area is less than 18 cm² type a response show your work

Explanation:

Step1: Recall trapezoid area formula

The area formula for a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height. Here, $a = 4$ cm, $b = 8$ cm, and $h=x$ cm, so $A=\frac{(4 + 8)x}{2}$.

Step2: Simplify the area formula

$\frac{(4 + 8)x}{2}=\frac{12x}{2}=6x$.

Step3: Set up the inequality

Since the area is less than $18$ cm², we have the inequality $6x<18$.

Step4: Solve the inequality

Divide both sides of the inequality $6x<18$ by $6$. We get $x < 3$. Also, since $x$ represents a dimension, $x>0$.

Answer:

$0 < x<3$