o find the area of the geometric shape with the given vertices, you can use the shoelace formula. The shoelace formula is a method used to calculate the area of a polygon when the coordinates of its vertices are known. Here are the steps to find the area using the shoelace formula: 1. Write down the coordinates of the vertices in order, either clockwise or counterclockwise. In this case, the vertices are (0,0), (10,2), (13,8), and (3,6). 2. Multiply each x-coordinate by the y-coordinate of the next vertex in the sequence and write down the products. For example: - (0 x 2) = 0 - (10 x 8) = 80 - (13 x 6) = 78 - (3 x 0) = 0 3. Multiply each y-coordinate by the x-coordinate of the next vertex in the sequence and write down the products. For example: - (0 x 10) = 0 - (2 x 13) = 26 - (8 x 3) = 24 - (6 x 0) = 0 4. Add up all the products from Step 2 and subtract the sum of the products from Step 3. In this case: - (0 + 80 + 78 + 0) - (0 + 26 + 24 + 0) = 158 - 50 = 108 5. Take the absolute value of the result from Step 4. This ensures that the area is always positive. In this case, the area is 108. Therefore, the area of the geometric shape with the given vertices is 108 square units.