What is the area of the quadrilateral with co-ordinates (3, 4), (4, 2), (1, 4) and (6, 2)?

To find the area of the quadrilateral with coordinates (3, 4), (4, 2), (1, 4), and (6, 2), we can use the Shoelace Formula.

Step 1: Write down the coordinates in a clockwise order: (3, 4), (4, 2), (1, 4), (6, 2), (3, 4)

Step 2: Multiply the x-coordinate of each point by the y-coordinate of the next point, and subtract the product of the y-coordinate of each point by the x-coordinate of the next point. Add up all these values.

(3 * 2) - (4 * 4) = -10 (4 * 4) - (1 * 2) = 14 (1 * 2) - (6 * 4) = -22 (6 * 4) - (3 * 2) = 18

Step 3: Take the absolute value of the sum and divide it by 2 to get the area.

|(-10 + 14 - 22 + 18)| / 2 = 20 / 2 = 10

Therefore, the area of the quadrilateral is 10 square units.