Question

1. trapezoid abcd find side lengths first! ab = 3 ad = 5 dc = 6 bc=\sqrt{(-3 + 6)^2+(3 - 8)^2}= bc = 5.8 3+5+6+5.8= perimeter = 19.8 area = ____

Explanation:

Step1: Recall trapezoid area formula

The formula for the area of a trapezoid is $A=\frac{1}{2}(a + b)h$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height. Here, the parallel sides are $AB = 3$ and $DC=6$, and the height (perpendicular distance between the parallel sides) can be considered in terms of the vertical distance in the coordinate - plane. Let's assume the height is the vertical distance between the parallel lines containing $AB$ and $DC$.

Step2: Calculate the area

We know that $a = 3$, $b = 6$. Let's assume the height $h$ is the vertical distance between the parallel sides. From the side - length calculations, we can consider the height as the vertical distance. Using the formula $A=\frac{1}{2}(a + b)h$, substituting $a = 3$, $b = 6$ and assuming the height based on the geometric setup (the vertical separation between the parallel sides), we have $A=\frac{1}{2}(3 + 6)\times5=\frac{1}{2}\times9\times5 = 22.5$.

Answer:

$22.5$