Question

what is the area of the trapezoid? square units

Explanation:

Step1: Calculate the lengths of the two bases

The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) with the same \(y -\)coordinate is \(d=\vert x_2 - x_1\vert\).
For the upper - base:
The points are \((-8,-2)\) and \((6,-2)\). Using the distance formula \(b_1=\vert6-(-8)\vert=\vert6 + 8\vert = 14\).
For the lower - base:
The points are \((-4,-7)\) and \((2,-7)\). Using the distance formula \(b_2=\vert2-(-4)\vert=\vert2 + 4\vert=6\).

Step2: Calculate the height

The height \(h\) is the vertical distance between the two parallel sides (bases).
The \(y -\)coordinates of the two bases are \(y=-2\) and \(y = - 7\). Using the distance formula for points with the same \(x -\)coordinate (or vertical distance formula \(h=\vert y_2-y_1\vert\)), \(h=\vert-2-(-7)\vert=\vert-2 + 7\vert=5\).

Step3: Use the trapezoid area formula

The area formula of a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\).
Substitute \(b_1 = 14\), \(b_2=6\), and \(h = 5\) into the formula:
\(A=\frac{(14 + 6)\times5}{2}=\frac{20\times5}{2}\).
First, calculate \(20\times5=100\), then \(\frac{100}{2}=50\).

Answer:

\(50\)