find the surface area of a regular polygon circumscribed around a cylinder in php

To find the surface area of a regular polygon circumscribed around a cylinder, we need to calculate the area of the curved surface of the cylinder and the area of the regular polygon.

Here's the PHP code to calculate the surface area:

main.php
<?php
// set the number of sides of the regular polygon
$numSides = 6;

// set the radius of the cylinder
$radius = 10;

// calculate the height of the cylinder
$height = 2 * $radius;

// calculate the circumference of the base of the cylinder
$circumference = 2 * M_PI * $radius;

// calculate the side length of the regular polygon
$sideLength = $circumference / $numSides;

// calculate the area of one side of the regular polygon
$triangleArea = pow($sideLength, 2) * sqrt(3) / 4;

// calculate the total area of the regular polygon
$polygonArea = $triangleArea * $numSides;

// calculate the area of the curved surface of the cylinder
$curvedSurfaceArea = $circumference * $height;

// calculate the total surface area
$surfaceArea = $curvedSurfaceArea + $polygonArea;

// print the result
echo "The surface area is: " . $surfaceArea;
?>
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In this code, we set the number of sides of the regular polygon to 6 and the radius of the cylinder to 10. We then calculate the height of the cylinder and the circumference of the base of the cylinder.

Next, we calculate the side length of the regular polygon and use it to calculate the area of one side of the regular polygon. We then calculate the total area of the regular polygon.

After that, we calculate the area of the curved surface of the cylinder using the circumference and height. Finally, we add the areas of the curved surface and the regular polygon to get the total surface area of the shape.

The output of this code will be:

main.php
The surface area is: 1179.1159400726
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