find the surface area of a regular polygon inscribed in a cone in php

To find the surface area of a regular polygon inscribed in a cone, we need to calculate the area of the base and the lateral surface area.

The area of the base is simply the area of the regular polygon. Given the number of sides n, length of a side s and apothem (distance from centre of polygon to midpoint of any of its sides) a, the area A of the regular polygon is given by:

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$A = 0.5*n*s*a;
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The lateral surface area is the curved surface of the cone between the base and the apex. The lateral surface area L can be calculated using the slant height l and the perimeter of the base P. The slant height l can be calculated using the Pythagorean theorem as:

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$l = sqrt(r^2 + h^2);
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where r is the radius of the base of the cone and h is the height of the cone. The perimeter P of the base can be calculated using the formula:

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$P = n*s;
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where n is the number of sides and s is the length of a side. The lateral surface area L is given by:

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$L = 0.5*P*l;
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Putting it all together, we can calculate the total surface area T of the cone as the sum of the base area A and the lateral surface area L:

main.php
function surface_area_regular_polygon_inscribed_cone($n, $s, $a, $h) {
    // Calculate base area
    $A = 0.5 * $n * $s * $a;
    
    // Calculate slant height
    $r = ($s / 2) * (1 / tan(M_PI / $n));
    $l = sqrt(pow($r, 2) + pow($h, 2));
    
    // Calculate perimeter of base
    $P = $n * $s;
    
    // Calculate lateral surface area
    $L = 0.5 * $P * $l;
    
    // Calculate total surface area
    $T = $A + $L;
    
    return $T;
}
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To use this function, simply pass in the number of sides n, length of a side s, apothem a and height of the cone h. The function returns the total surface area T of the cone in the same units as the inputs.