Question

the area of the trapezoid is 1.5 square millimeters. what is the trapezoids height, h? h = millimeters

Explanation:

Step1: Recall trapezoid area formula

The area formula of a trapezoid is $A=\frac{(a + b)h}{2}$, where $A$ is the area, $a$ and $b$ are the lengths of the parallel - sides, and $h$ is the height. Here, $a = 0.8$ mm, $b = 1.7$ mm, and $A=1.5$ square mm.

Step2: Rearrange the formula to solve for $h$

Starting from $A=\frac{(a + b)h}{2}$, we first multiply both sides by 2 to get $2A=(a + b)h$. Then, we divide both sides by $(a + b)$ to isolate $h$. So, $h=\frac{2A}{a + b}$.

Step3: Substitute the given values

Substitute $A = 1.5$, $a = 0.8$, and $b = 1.7$ into the formula $h=\frac{2A}{a + b}$. We have $h=\frac{2\times1.5}{0.8 + 1.7}$. First, calculate the numerator: $2\times1.5 = 3$. Then, calculate the denominator: $0.8+1.7 = 2.5$. So, $h=\frac{3}{2.5}=1.2$ mm.

Answer:

$1.2$