# 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 atleast 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 * heightSo height can be calculated as :

height = (2 * area)/ baseMinimum height is the ceil of the

height obtained using above formula.

## 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; ` `} ` |

*chevron_right*

*filter_none*

## 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. ` |

*chevron_right*

*filter_none*

## 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)) ` |

*chevron_right*

*filter_none*

## 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. ` |

*chevron_right*

*filter_none*

## 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. ` `?> ` |

*chevron_right*

*filter_none*

**Output :**

Minimum height is 4

## Recommended Posts:

- Maximum height when coins are arranged in a triangle
- Area of Reuleaux Triangle
- Check if right triangle possible from given area and hypotenuse
- Area of Circumcircle of a Right Angled Triangle
- Program to find area of a triangle
- Area of a triangle inside a parallelogram
- Area of Incircle of a Right Angled Triangle
- Maximum area of triangle having different vertex colors
- Area of circle which is inscribed in equilateral triangle
- Area of the Largest Triangle inscribed in a Hexagon
- Area of a largest square fit in a right angle triangle
- Area of largest triangle that can be inscribed within a rectangle
- Find the altitude and area of an isosceles triangle
- Program to calculate area and perimeter of equilateral triangle
- Find area of triangle if two vectors of two adjacent sides are given

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.