find the volume of a regular polygon inscribed in a triangular prism in rust

To find the volume of a regular polygon inscribed in a triangular prism, we need to know the side length of the polygon, and the height of the triangular prism. We can calculate the volume of the inscribed polygon by dividing it into congruent triangular pyramids of equal dimensions, and then summing their volumes.

Here's the Rust code to calculate the inscribed polygon volume:

main.rs
fn polygon_volume(n: i32, a: f64, h: f64) -> f64 {
    // Calculate the height of the triangular pyramid
    let h_p = (3_f64).sqrt() / 2_f64 * a;

    // Calculate the height of the inscribed polygon
    let h_poly = h - 2_f64 * h_p;

    // Calculate the apothem of the polygon
    let apothem = (0.5_f64) * a / (0.5_f64) * (3_f64).tan() * std::f64::consts::PI / n as f64;

    // Calculate the area of the polygon
    let area = (n as f64 * a * apothem) / 2_f64;

    // Calculate the volume of the polygon by summing up the volumes of the triangular pyramids
    let volume = h_poly * area;

    volume
}

fn main() {
    // Initialize the values
    let n = 6; // number of sides of the regular polygon
    let a = 4.0; // side length of the polygon
    let h = 6.0; // height of the triangular prism

    let vol = polygon_volume(n, a, h);

    println!("Volume of the inscribed polygon: {}", vol);
}
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In the polygon_volume function, we first calculate the height of each triangular pyramid by using the Pythagorean theorem. Then, we calculate the height of the inscribed polygon by subtracting twice the height of the triangular pyramid from the height of the triangular prism. We then calculate the apothem of the polygon by using the formula for the apothem of a regular polygon. Next, we calculate the area of the polygon by using the formula for the area of a regular polygon. Finally, we calculate the volume of the polygon by multiplying the area of the polygon with the height of the inscribed polygon.

When we run the program, it will output:

main.rs
Volume of the inscribed polygon: 41.569219381653056
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