Question

what is the area, in square units, of trapezoid abcd?

Explanation:

Step1: Identify the formula for the area of a trapezoid

The formula for the area of a trapezoid is $A=\frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the parallel - sides and $h$ is the height between them.

Step2: Determine the lengths of the parallel - sides and the height from the graph

By counting the grid - squares:
The length of the top - parallel side $b_1$ (the distance between $B(-8,4)$ and $C(8,4)$) is $|8-(-8)|=16$ units.
The length of the bottom - parallel side $b_2$ (the distance between $A(-6,-4)$ and $D(7,-4)$) is $|7-(-6)| = 13$ units.
The height $h$ (the vertical distance between the two parallel lines) is $|4-(-4)|=8$ units.

Step3: Substitute the values into the formula

$A=\frac{1}{2}(16 + 13)\times8$.
First, calculate the sum of the parallel sides: $16+13 = 29$.
Then, multiply by $\frac{1}{2}$ and 8: $A=\frac{1}{2}\times29\times8=29\times4 = 116$ square units.

Answer:

116