Final answer:
To find the area of the polygon with the given vertices A(2,2), B(2,7), C(8,7), and D(4,2), you can divide it into two triangles and calculate their areas using the formula A = 0.5 * base * height. Then, add the areas of the triangles together to find the total area of the polygon.
Step-by-step explanation:
To find the area of a polygon with given vertices, you can use the formula for the area of a triangle. In this case, you can divide the polygon into two triangles, ABC and ACD. Then, calculate the area of each triangle using the formula A = 0.5 * base * height.
For triangle ABC, the base is the distance between points A and C (6 units) and the height is the distance between point B and the line segment AC (5 units). So, the area of triangle ABC is 0.5 * 6 * 5 = 15 square units.
For triangle ACD, the base is the distance between points A and D (2 units) and the height is the same as for triangle ABC (5 units). So, the area of triangle ACD is 0.5 * 2 * 5 = 5 square units.
Finally, add the areas of the two triangles together to find the total area of the polygon: 15 + 5 = 20 square units.