# PHP Exercises: Compute the area of the polygon

## PHP: Exercise-73 with Solution

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

**Pictorial Presentation: **

**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.

**Sample Solution: **-

**PHP Code:**

```
<?php
calc();
function calc() {
$points = array();
while ($line = trim(fgets(STDIN))) {
list($x, $y) = explode(',', $line);
$points[] = new Point($x, $y);
}
$sum = 0;
$o = $points[0];
for ($i = 1; $i < count($points) - 1; $i++) {
$p1 = $points[$i];
$p2 = $points[$i+1];
$T = new Triangle($o, $p1, $p2);
$sum += $T->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

**Flowchart: **

**PHP Code Editor:**

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## PHP: Tips of the Day

**Returns all elements in an array except for the first one**

Example:

<?php function tips_tail($items) { return count($items) > 1 ? array_slice($items, 1) : $items; } print_r(tips_tail([1, 5, 7])); ?>

Output:

Array ( [0] => 5 [1] => 7 )

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