Minimum height of a triangle with given base and area

Given two integers a and b, find the smallest possible height such that a triangle of at least area “a” and base “b” can be formed.

Examples:

Input : a = 2, b = 2
Output : Minimum height of triangle is 2

Explanation: 

Input : a = 8, b = 4
Output : Minimum height of triangle is 4

Minimum height of Triangle with base “b” and area “a” can be evaluated by having the knowledge of the relationship between the three.

The relation between area, base and 
height is: 
area = (1/2) * base * height
So height can be calculated as : 
height = (2 * area)/ base
Minimum height is the ceil of the 
height obtained using above formula.

Example:

C++

#include <bits/stdc++.h>
using namespace std;
// function to calculate minimum height of
// triangle
int minHeight(int base, int area)
{
    return ceil((float)(2 * area) / base);
}

int main()
{
    int base = 4, area = 8;
    cout << "Minimum height is " << minHeight(base, area)
         << endl;

    return 0;
}

Java

// Java code Minimum height of a
// triangle with given base and area

class GFG {

    // function to calculate minimum height of
    // triangle
    static double minHeight(double base, double area)
    {
        double d = (2 * area) / base;
        return Math.ceil(d);
    }

    // Driver code
    public static void main (String[] args)
    {
        double base = 4, area = 8;
        System.out.println("Minimum height is "+
                            minHeight(base, area));
    }
}
// This code is contributed by Anant Agarwal.

Python

# Python Program to find minimum height of triangle
import math

def minHeight(area,base):
        return math.ceil((2*area)/base)

# Driver code
area = 8
base = 4
height = minHeight(area, base)
print("Minimum height is %d" % (height))

C#

// C# program to find minimum height of
// a triangle with given base and area
using System;

public class GFG {

    // function to calculate minimum
    // height of triangle
    static int minHeight(int b_ase, int area)
    {
        return (int)Math.Round((float)(2 * area) / b_ase);
    }

    // Driver function
    static public void Main()
    {
        int b_ase = 4, area = 8;
        Console.WriteLine("Minimum height is "
                        + minHeight(b_ase, area));
    }
}

// This code is contributed by vt_m.

PHP

<?php

// function to calculate minimum
// height of triangle
function minHeight($base, $area)
{
    return ceil((2 * $area) / $base);
}

// Driver Code
$base = 4;$area = 8;
echo "Minimum height is ",
      minHeight($base, $area);

// This code is contributed by anuj_67.
?>

Javascript

<script>

// function to calculate minimum height of
// triangle
function minHeight( base,  area){
    return Math.ceil((2*area)/base);
}


    let base = 4, area = 8;

    document.write( "Minimum height is "
         +minHeight(base, area));

// This code contributed by aashish1995

</script>

Output :

Minimum height is 4

Time complexity: O(1)
Auxiliary Space: O(1)

Approach#2: Using Heron’s formula

Heron’s formula is an alternative way to calculate the area of a triangle. Given the lengths of all three sides of a triangle (a, b, and c), the area can be calculated using the following formula: Area = ?(s(s-a)(s-b)(s-c)) where s is the semi perimeter of the triangle, which is half the perimeter: s = (a + b + c) / 2 Using this formula, we can rearrange it to solve for the height of the triangle in terms of the base and area: Height = (2 * Area) / Base

Algorithm:

1. Calculate the semiperimeter s using s = (a + b + c) / 2
2. Calculate the area of the triangle using Heron’s formula
3. Calculate the height of the triangle using Height = (2 * Area) / Base
4. Return the height as the output

C++

#include <cmath>
#include <iostream>

using namespace std;

double minimumHeight(double base, double area)
{
    double s = base / 2;

    // Calculate the area of the triangle using Heron's
    // formula
    double area_tri = (4 * pow(area, 2)) / pow(base, 2);

    // Calculate the height of the triangle using Height =
    // (2 * Area) / Base
    double height = (2 * area) / base;
    return height;
}

int main()
{
    double area = 8;
    double base = 4;
    cout << minimumHeight(base, area);
    return 0;
}

Java

public class MinimumHeight {
  public static double minimumHeight(double base, double area) {
    double s = base / 2;
    // Calculate the area of the triangle using Heron's formula
    double area_tri = (4 * Math.pow(area, 2)) / Math.pow(base, 2);

    // Calculate the height of the triangle using Height = (2 * Area) / Base
    double height = (2 * area) / base;
    return height;
  }

  public static void main(String[] args) {
    double area = 8;
    double base = 4;
    System.out.println(minimumHeight(base, area));
  }
}

Python3

def minimum_height(base, area):
  s = base / 2
  # Calculate the area of the triangle using Heron's formula
  area_tri = (4 * area**2) / (base**2)

  # Calculate the height of the triangle using Height = (2 * Area) / Base
  height = (2 * area) / base
  return height
area = 8
base = 4
print(minimum_height(base, area))

Javascript

function minimumHeight(base, area) {
  let s = base / 2;
  // Calculate the area of the triangle using Heron's formula
  let areaTri = (4 * Math.pow(area, 2)) / Math.pow(base, 2);

  // Calculate the height of the triangle using Height = (2 * Area) / Base
  let height = (2 * area) / base;
  return height;
}

let area = 8;
let base = 4;
console.log(minimumHeight(base, area));

Output

4.0

Time complexity: O(1)
Auxiliary Space: O(1)