Question

find the area of the trapezoid shown below

Explanation:

Step1: Recall trapezoid area formula

The area of a trapezoid is given by $\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h$, where $b_1$ and $b_2$ are the lengths of the two parallel bases, and $h$ is the height.

Step2: Identify given values

Here, $b_1 = 12$, $b_2 = 30$, and $h = 24$.

Step3: Substitute values into formula

$$ \text{Area} = \frac{1}{2} \times (12 + 30) \times 24 $$

Step4: Simplify the expression

First calculate the sum of the bases: $12 + 30 = 42$.
Then compute $\frac{1}{2} \times 42 = 21$.
Finally, $21 \times 24 = 504$.

Answer:

504