find the volume of a regular polygon inscribed in a pyramid in rust

To find the volume of a regular polygon inscribed in a pyramid, we can use the formula:

V = (1/3) * base area * height

where base area is the area of the regular polygon at the base of the pyramid, and height is the height of the pyramid.

Here's a Rust function that takes in the number of sides of the regular polygon, the length of each side, and the height of the pyramid, and returns the volume of the polygon inscribed in the pyramid:

main.rs
fn polygon_in_pyramid_volume(num_sides: u32, side_length: f64, pyramid_height: f64) -> f64 {
    let apothem = side_length / (2.0 * (std::f64::consts::PI / num_sides as f64).tan());
    let base_area = (num_sides as f64 * side_length * apothem) / 2.0;
    let volume = (1.0 / 3.0) * base_area * pyramid_height;
    volume
}
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This function first calculates the apothem (the distance from the center of the polygon to the midpoint of its sides), using the formula:

apothem = side_length / (2 * tan(pi / n))

where n is the number of sides and pi is the constant representing the value of pi.

It then calculates the base area using the formula for the area of a regular polygon:

area = (n * s * a) / 2

where s is the length of each side of the polygon, and a is the apothem.

Finally, it calculates the volume using the formula we started with.

Note that the function returns a floating-point number (of type f64). If you want to round the result to a certain number of decimal places, you can use the round() method on the resulting value, for example:

main.rs
let volume = polygon_in_pyramid_volume(6, 5.0, 10.0).round();
println!("The volume of the regular hexagon inscribed in the pyramid is {}.", volume);
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