Question

what is the missing length? area = 72.16 cm² a = centimeters

Explanation:

Step1: Recall triangle - area formula

The area formula for a triangle is $A=\frac{1}{2}bh$, where $A$ is the area, $b$ is the base, and $h$ is the height. Here, $b = 16.4$ cm, $A=72.16$ cm², and $h = a$.

Step2: Rearrange the formula to solve for $a$

Starting from $A=\frac{1}{2}bh$, we can solve for $h$ (which is $a$ in our case). First, multiply both sides of the equation by 2 to get $2A = bh$. Then, divide both sides by $b$: $a=h=\frac{2A}{b}$.

Step3: Substitute the given values

Substitute $A = 72.16$ cm² and $b = 16.4$ cm into the formula $a=\frac{2A}{b}$. So, $a=\frac{2\times72.16}{16.4}$.
First, calculate $2\times72.16 = 144.32$. Then, $\frac{144.32}{16.4}=8.8$ cm.

Answer:

$8.8$