Questions: Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure. A(-2,6), B(8,6), C(8,-3), D(5,-3), E(5,-7), F(2,-3), G(-2,-3)

Solution Steps

The points given are \( A(-2,6) \), \( B(8,6) \), \( C(8,-3) \), \( D(5,-3) \), \( E(5,-7) \), \( F(2,-3) \), and \( G(-2,-3) \). These points need to be connected in the order listed to form a closed figure.

The figure can be divided into simpler shapes to calculate the area. The points form a polygon that can be divided into rectangles and triangles.

1. Rectangle \(ABCD\):

   • Width = \(8 - (-2) = 10\)
   • Height = \(6 - (-3) = 9\)
   • Area = \(10 \times 9 = 90\)

2. Rectangle \(DEFG\):

   • Width = \(5 - (-2) = 7\)
   • Height = \(-3 - (-7) = 4\)
   • Area = \(7 \times 4 = 28\)

3. Triangle \(CDF\):

   • Base = \(8 - 5 = 3\)
   • Height = \(-3 - (-7) = 4\)
   • Area = \(\frac{1}{2} \times 3 \times 4 = 6\)

The total area of the figure is the sum of the areas of these shapes: \[ \text{Total Area} = 90 + 28 - 6 = 112 \]

Final Answer