A convex polygon is a simple polygon in which no line segment between two points on the boundary ever goes outside the polygon

hamza

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2022-05-18

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A convex polygon is a simple polygon in which no line segment between two points on the boundary ever goes outside the polygon. Equivalently, it is a simple polygon whose interior is a convex set. In a convex polygon, all interior angles are less than or equal to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees.
Write a PHP program that compute the area of the polygon . The vertices have the names vertex 1, vertex 2, vertex 3, ... vertex n according to the order of edge connections. However, n is 3 or more and 20 or less. You can also use the following formula to calculate the area S from the lengths a, b, and c of the triangle's three sides.

Input: Multiple character strings are given. One string is given per line

Input:
Input is given in the following format.
x1 , y1
x2 , y2
:
xn , yn
xi , yi are real numbers representing the x and y coordinates of vertex i , respectively.

Php programming,

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hamza

2022-05-18

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getArea();
    }
    echo "Area of the polygon:\n";
    echo $sum . "\n";
}
 
class Triangle {
    public $A, $B, $C;
    public $a, $b, $c;
 
    public function __construct(Point $A, Point $B, Point $C) {
        $this->A = $A;
        $this->B = $B;
        $this->C = $C;
 
        $this->a = $B->distanceFrom($C);
        $this->b = $C->distanceFrom($A);
        $this->c = $A->distanceFrom($B);
    }
 
    public function getArea() {
        $z = ($this->a + $this->b + $this->c) / 2;
        return sqrt($z * ($z - $this->a) * ($z - $this->b) * ($z - $this->c));
    }
}
 
class Point {
    public $x, $y;
 
    public function __construct($x, $y) {
        $this->x = $x;
        $this->y = $y;
    }
 
    public function distanceFrom(Point $p) {
        $dx = $this->x - $p->x;
        $dy = $this->y - $p->y;
        return sqrt($dx * $dx + $dy * $dy);
    }
}
?>

Sample Input:
1.0, 0.0
0.0, 0.0
1.0, 1.0
2.0, 0.0
-1.0, 1.0

Sample Output:

Area of the polygon:
1.5

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total answers (1)

A convex polygon is a simple polygon in which no line segment between two points on the boundary ever goes outside the polygon

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