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