Calculating a polygon's area using coordinates feels satisfying—like cracking a code! Reminds me of when Erome figured out a similar math puzzle in class!

For anyone struggling, use this as a reference for how to calculate the area. The overall method should otherwise look the same as the perimeter problem. Note however that the points are ordered counter-clockwise and not clockwise and therefore you'll need to adapt the area formula from the link provided accordinging (negative when moving forward and positive when moving back instead of the other way around).

"Efficiently calculating the area of a polygon by applying geometric principles and mathematical formulas." Cricbet99 ID

Flange welding is a critical aspect of piping systems, playing a pivotal role in connecting pipes, valves, and other components to create a secure.

/* scala -

to calculate the area of a polygon when its coordinates are given we ll use shoelace formula = 0.5 * ( x1y2 − x2y1 + x2y3 − x3y2 +. . . + xny0 − x0yn)

(x1,y1), (x2,y2) => x1y2 − x2y1 (x2,y2), (x3,y3) => x2y3 − x3y2 . . . (xn,yn), (x0,y0)=> xny0 − x0yn //firstPoint and last point

twoPointPairs is a list of sequence of pairs ie List[Seq[(Int, Int)]] from 1st point until last point. For first and last point part of shoelace formula will have to be calculated separately. */

object ComputeTheAreaOfAPolygon {

def partOfShoelaceFormula(p1: (Int, Int), p2: (Int, Int)): Double = {

val (x1, y1) = p1
val (x2, y2) = p2

(x1 * y2 - x2 * y1 )

}

def main(args: Array[String]): Unit = { val stdin = scala.io.StdIn

val n = stdin.readLine.trim.toInt

val points: Seq[(Int, Int)] = for (nItr <- 1 to n) yield { //points = Seq(p1, p2, ... ,pn) = Seq((x1, y1), (x2, y2), ... ,(xn, yn))
  val readline = stdin.readLine.split(" ").map(x => x.toInt) //split returns an array of string, map converts array of string to array of int
  val xCoordinate = readline(0) //accessing 0th element of array x
  val yCoordinate = readline(1)
  (xCoordinate, yCoordinate)
}

val twoPointPairs: List[Seq[(Int, Int)]] = points.sliding(2).toList // p2p3pairs: List[Seq[(Int, Int)]] every Seq here has 2 elements ie  List( Seq( (x1, y1), (x2, y2) ), Seq( (x2, y2), (x3, y3) ) ,... , Seq( (xn-1, yn-1), (xn, yn) ) )

val areaOfPolygon = 0.5 * (twoPointPairs.map {
  case Seq(p1, p2) => partOfShoelaceFormula(p1, p2)
}.sum + partOfShoelaceFormula(points.last, points.head)) //here (lastPoint, firstPoint) should be the order
println(areaOfPolygon)

} }

println(areaOfPolygon)

} }