In programming, being able to find a triangle area is useful for many reasons. This can help you understand logic and understand syntax, and this is a common problem of programming used in school assignments. There are also many real -world applications, such as computer graphics, geometry -based imitation, or construction calculations.
In this article, we will see a common problem: We are given the dimensions of a triangle, and our job is to calculate its area. You can calculate the area of ​​a triangle using different formulas, depending on the information you have about the triangle. Here, you are going to learn how to do it using PHP.
After reading this tutorial:
You will understand the basic logic behind calculating the area of ​​the triangle.
You will know how to write the PHP code, which calculates the triangle area using the default and the values ​​enrolled in the user.
You will know how to apply this logic in small projects and assignments.
The table of content
Provisions
If you have some information about some things you will understand this guide more easily:
Primary pHP
To fully understand this issue, you will need to know the basic PHP syntax. If you know that you have to write a simple Eco statement or create a variable in PHP, you should go.
Local PHP environment
You should successfully run the PHP code, you should keep local PHP development on your machine, such as XAMPP or WAMP. You can use online PHP editors such as PHP Fidel or online GDB to run a PHP script without installation.
In this tutorial we are going to find three perspectives to determine the triangle area in the PHP based on the amount of information available about the triangle.
Base and height formula approach: This approach applies when you have a base and height of standing in the problem.
Heron’s Formula: When you have the length of all three sides of the triangle, this approach is used to calculate the area of ​​the triangle.
The egotistical formula approach: This approach is applied to the problem when your length is included between two sides and the angle.
First, let’s go back to the math class and use some direct formulas to find this area.
Find an area of ​​triangle using direct formulas
Example 1:
In this first example, you are given a triangle input base and height. You have to return the triangle area. For example, you will use the formula directly to calculate the area of ​​the triangle.
Input:
Twenty = 5,
Height = 10
You can calculate the triangle area using the formula:
$$ Area = (twenty * height) / 2 $$
So, if you plug your values, you get: (5* 10) / 2 = 25.
Output:
Area = 25
Example 2:
In this second example, you have been given the length of an angle between two sides of the triangle and between them. You have to return the triangle area. In this example, you will use another direct formula to calculate the triangle area.
Input:
Side A = 7, Side B = 9, angle between them = 60 °
In this case, you will use the formula:
$$ area = (1/2) now * sin (angle). $$
Then just replace the values ​​that you are given to find out.
Output:
Area = 27.33 (approximately)
Now look at some different ways to find the triangle area using PHP.
Find an area of ​​triangle using base and height
This is the easiest and direct approach to calculate the area of ​​the triangle when you know the base and height. In this approach, you will directly put values ​​in the formula and find an area of ​​triangles – but you will do it with a PHP code.
First, explain the base and height of the triangle. Then apply the formula for the triangle area. As we saw above, the formula of the triangle area is:
$$ Area = (twenty * height) / 2 $$
After calculating the triangle area, output the answer.
Well, so here we can implement it in PHP:
$base = 5;
$height = 10;
$area = ($base * $height) / 2;
echo "The area of the triangle is: " . $area . " square units.";
?>
Output:
The area of ​​the triangle is 25 square units.
In the aforementioned code, we first start the triangle base and height in two variables. Then we plug these values ​​into the area’s formula. The PHP calculates the area of ​​the triangle and responds.
The complexity of timeIn the above point of view, we are using the formula directly to calculate and return the triangle area, so the complexity of the time will remain permanently at O ​​(1). The complexity of the permanent time is effective because it will remain permanent, regardless of its base and height size or values.
Space complexity: Space complexity will be O (1). The space used by the aforementioned program is permanent, which ensures the minimum use of memory. This space complexity is ideal in an environment where memory performance is a priority.
We use the above point of view when we have the length and height of the triangle (whether directly given or easily measured in the right angle triangle). This method works best for the right corner triangle.
Find an area of ​​triangle using Heron’s formula
Heron’s formula is named after the Greek mathematician, named Heron of Alexandria. Heron’s formula is useful when you know the length of all three sides of the triangle and you want to calculate this area without needing height. This formula works for any type of triangle, which includes scaline triangles (triangles along all different lengths).
Here is Heron’s formula to calculate a triangle area:
$$ √s (s – a) (s – b) (s – c) $$
Where:
S = semi -perimemat = (A+B+C)/2 is the semi -pirmial of the triangle.
A, B, and C are on the sides.
First, we explain the three sides of the triangle. Then, we check all three terms The theory of triangle inequality It has been said that if the combination of two sides is higher than the third, then it is a valid triangle, and the given sides can form a triangle.
We can calculate the semi -pin of the triangle using the formula S = A+B+C/2. Then we can apply Heron’s formula to calculate the area. After calculating the area, then out the answer.
Here is how you can enforce it in a PHP:
$a = 7;
$b = 9;
$c = 10;
if (($a + $b > $c) && ($a + $c > $b) && ($b + $c > $a)) {
$s = ($a + $b + $c) / 2;
$area = sqrt($s * ($s - $a) * ($s - $b) * ($s - $c));
echo "The area of the triangle is: " . $area . " square units.";
} else {
echo "The given sides do not form a valid triangle.";
}
?>
Output:
The area of ​​the triangle is: 27.321 square units.
In the aforementioned code, we first produce three variables to store the length of the triangle, and check whether the parties given a valid triangle or use the theory of triangle inequality. We then calculate the semi -parameter using the formula: S = A + B + C / 2. We have put the price of semi -peter and length in the Heron’s formula to calculate this area and the length of each side. The area of ​​the triangle has been returned after calculating using the formula.
The complexity of time: There is a total number of operations such as increase, reduction, multiplication and square root. These operations do not rely on input size because they are performed only in a fixed number. This means that the complexity of the time is permanent o (1).
Space complexity: We have used a certain number of variables to calculate the triangle area. We have not used any additional data structures such as rows or items. The use of memory in the program is permanent, which is better for a low memory environment. The complexity of the space is permanent o (1).
When the length of each side is given, this approach works best. This approach is mainly used for the scalcin or the iscellus triangle where the height is not directly given. This approach can work for any type of triangle, however – scalcin, iosylus, or acne.
Find an area of ​​a triangle using two sides and add angle to it (trigonometric formula)
In this point of view, we will see a different change of the problem. When you know two sides of a triangle and the angle included between them, you can calculate the area using this formula:
$$ area = 1/2 × A × B × Sin (θ) $$
Where:
A and B are lengths on both sides.
Degrees is the angle between the two sides, measured in a degree or redin.
Using the aforementioned formula, you can calculate the triangle area without the need for its height. First, you explain the angle between both sides of the triangle and between them. Then you turn the angle from the degree to Redin when needed (in PHP, you can use the DEG2 Red ()) to convert degrees into Redin). Then you apply the formula.
After calculating the triangle area, conclude.
How to implement this in PHP is:
$a = 7;
$b = 9;
$angle = 60;
$angle_in_radians = deg2rad($angle);
$area = 0.5 * $a * $b * sin($angle_in_radians);
echo "The area of the triangle is: " . $area . " square units.";
?>
Output:
The area of ​​the triangle is: 27.321 square units.
Explanation:
In the above case, we are using the formula:
The area of ​​the triangle = 1/2 × a × b × sin (θ)
And we are converting the following values ​​into formulas:
Area = 1/2 × 7 × 9 × sin (60 ∘) ≈ 27.321
In the code, we announced two variables to store the length of both sides of the triangle, and the variable $angle Including the angle in degrees. We used to use deg2rad()A PhP Built -in Function that converts angles from degrees to Redin. Then, we applied the original formula: 1/2 × 7 × 9 × sin (60 %). PHP has stored in the final response $area Variable
The complexity of time: When we are using direct formulas to calculate the area of ​​the triangle, the length of two parties and the angle is given between them. The complexity of the permanent time is O (1).
Space complexitySimilarly, it does not take any extra space or uses any data structure. It uses the same variable to store the result, which is why space complexity is permanent O (1).
This approach is the best Perfect of the problem, which is known as two sides and the added angle (angle between these parties). You can use it when you can’t easily calculate the height of the triangle. This issue has real -life requests in geometry problems, CAD applications, or physics impressions. This method is very accurate and does not require lengths on all sides.
Conclusion
In this article, you have learned how you can calculate a triangle area, to use both manually and PHP. You have seen different perspectives and have learned that you have better about the information you have. First, we discussed the base and height approach, then looked at Heron’s formula, and finally examined how to handle things when two parties and the added angle were given.
Understanding the logic behind each of them helps you make the right choice based on the data given to you.