Question

find the area of the trapezoid shown below

Explanation:

Step1: Recall trapezoid area formula

The formula for the area of a trapezoid is $A = \frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the two parallel sides (bases), and $h$ is the height (the perpendicular distance between the bases).

Step2: Identify values of a, b, h

From the diagram, $a = 11.4$, $b = 28.5$, and $h = 22.8$.

Step3: Substitute into the formula

Substitute the values into the formula: $A=\frac{(11.4 + 28.5)\times22.8}{2}$
First, calculate the sum of the bases: $11.4+28.5 = 39.9$
Then, multiply by the height: $39.9\times22.8=39.9\times22 + 39.9\times0.8=877.8+31.92 = 909.72$
Finally, divide by 2: $\frac{909.72}{2}=454.86$

Answer:

The area of the trapezoid is $454.86$.