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Ruslan López
Asked: 2020-01-13 23:53:55 +0800 CST 2020-01-13 23:53:55 +0800 CST

Calculate the area of ​​a triangle

  • 772

I am trying to calculate the area of ​​a triangle positioned on cartesian coordinates.

The triangle is formed from three points:

  • a
  • b
  • c

Each point has two coordinates:

  • x
  • Y

My logic is the following:

  1. calculate the distance between point a and point b call it base
  2. calculate a point exactly in the middle of a and b (bisector I think it is called)
  3. get the distance between midpoint of a and b and point c and call it height
  4. Calculate the area with the formula base times height over two

graphic representation of my logic

The logic seems appropriate to me, but I'm not passing the unit tests in the exercise.

This is my code:

function distance(x1,x2,y1,y2){
  return Math.sqrt(Math.pow((x2-x1),2) + Math.pow((y2-y1),2));
}

function area(b,h){
  return (b*h)/2;
}

function midlePoint(x1,x2,y1,y2){
  return new Point((x1+x2)/2,(y1+y2)/2);
}

function triangleArea(triangle){
  var {a,b,c} = triangle;
  var {x:x1,y:y1} = a;
  var {x:x2,y:y2} = b;
  var base = distance(x1,x2,y1,y2);
  console.log(base);
  var {x:midlex,y:midley} = midlePoint(x1,x2,y1,y2);
  var {x:x3,y:y3} = c;
  var height = distance( midlex,x3,midley,y3);
  console.log(height);
  return area(base,height);
}

These are the unit tests:

Test.assertEquals(+triangleArea(new Triangle(new Point(10, 10), new Point(40, 10), new Point(10, 50))).toFixed(6), 600)
Test.assertEquals(+triangleArea(new Triangle(new Point(15, -10), new Point(40, 20), new Point(20, 50))).toFixed(6), 675)

What will be the problem?

javascript

1 Answers

  1. Best Answer

    ISSUE

    Your problem is that you mistakenly assume that the height of your triangle passes through the midpoint of what you set as the base. Your logic holds only for isosceles triangles and when you choose the base properly.

    SOLUTION

    To calculate the area of ​​any triangle, given its vertices, you must use a different algorithm than the one you are trying to implement.

    The formula is given by:

    Área = (1/2)*(|nAB·AC|)

    Where |nAB·AC|is the absolute value of the dot product or scalar product of the vectors nABand AC. Being nABthe normal vector (perpendicular) toAB

    Step 1. Calculate the vectorAB: (Xb - Xa, Yb - Ya) = (Xab,Yab)

    Step 2. You calculate the normal vector to AB (it is the direction of the vector perpendicular to AB) nAB: (Xn, Yn) = (Yab, -Xab)

    Step 3. Calculate the vectorAC: (Xc - Xa, Yc - Ya) = (Xac,Yac)

    Step 4. Calculate the dot product (scalar product) of the vectors nAB and AC: (Xn * Xac) + (Yn * Yac)

    Step 5. You calculate the Area of ​​the triangle applying the formula: A = (1/2)(|scalarproduct|)

    RESULT

    How can your role be? Well, that's up to you, I'll just give you an example:

    var a = {x: 2, y: 0}
var b = {x: 3, y: 4}
var c = {x: -2, y: 5}

function vectorDireccion(v,w) {
  return {x: w.x-v.x, y: w.y - v.y}
}

function productoEscalar(v,w) {
  return (v.x * w.x) + (v.y * w.y);
}

function vectorNormal(v) {
  return {x: v.y, y: -v.x}
}

function moduloEscalar(escalar) {
  return escalar < 0 ? (-1 * escalar) : escalar;
}

function calcAreaTriangVertices(a, b, c) {
  var vecAB = vectorDireccion(a, b);
  var vecNAB = vectorNormal(vecAB);
  var vecAC = vectorDireccion(a, c);
  var pEscalar = productoEscalar(vecNAB, vecAC);
  return ((1/2) * moduloEscalar(pEscalar));
}

var area = calcAreaTriangVertices(a, b, c);

console.log(area);

    I hope this clears your doubt.

    Cheers

    References:

    Isosceles triangle - Wikipedia

    Scalar Product - Wikipedia

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