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Minimum height of a triangle with given base and area
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Program to calculate area and perimeter of equilateral triangle

Last Updated : 17 Feb, 2023
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An equilateral triangle is a triangle in which all three sides and angles are equal. All three internal angles of equilateral triangle measures 60 degree.

  • If we know the length of each sides of equilateral triangle, then we can use below mentioned formula to calculate area of equilateral triangle.
Area of Equilateral Triangle = (sqrt(3)/4) * a * a
  • If we know the length of altitude of equilateral triangle along with the length of side, then we can use below mentioned formula to calculate it's area.
Area of Equilateral Triangle = (1/2) x Side x Altitude

Perimeter of Equilateral Triangle :

Perimeter of Equilateral Triangle :  3 X a

How does the area formula work?
Let us take a look at below diagram. We know are of a triangle is 1/2 * base * height. The value of h is sqrt(a2 – (a/2)2) = sqrt(3) * a / 2. So the area becomes 1/2 * a * (sqrt(3) * a / 2) = (sqrt(3)/4) * a * a

 

Examples:

Input : side = 4  Output : Area of Equilateral Triangle: 6.9282          Perimeter of Equilateral Triangle: 12  Input : side = 12  Output : Area of Equilateral Triangle: 62.3538          Perimeter of Equilateral Triangle: 36
C++ 
// CPP program to find area // and perimeter of equilateral triangle #include <bits/stdc++.h> using namespace std;  // Function to calculate Area // of equilateral triangle float area_equi_triangle(float side) {     return sqrt(3) / 4 * side * side; }  // Function to calculate Perimeter // of equilateral triangle float peri_equi_triangle(float side) {     return 3 * side; }  // Driver Code int main() {     float side = 4;     cout << "Area of Equilateral Triangle: "         << area_equi_triangle(side) << endl;     cout << "Perimeter of Equilateral Triangle: "         << peri_equi_triangle(side);     return 0; }
Java 
// Java Program to find area and // perimeter of equilateral triangle import java.io.*;  class GFG {     // Function to calculate     // Area of equilateral triangle     static float area_equi_triangle(float side)     {          return (float)(((Math.sqrt(3)) / 4) *                         side * side);     }      // Function to calculate     // Perimeter of equilateral     // triangle     static float peri_equi_triangle(float side)     {         return 3 * side;     }          // Driver Code     public static void main(String arg[])     {         float side = 4;         System.out.print("Area of Equilateral Triangle:");         System.out.println(area_equi_triangle(side));         System.out.print("Perimeter of Equilateral Triangle:");         System.out.println(peri_equi_triangle(side));     } }  // This code is contributed // by Anant Agarwal.
Python 
# Python3 program to calculate Area and # Perimeter of equilateral Triangle  # Importing Math library for sqrt from math import *  # Function to calculate Area # of equilateral triangle def area_equilateral( side ):     area = (sqrt(3) / 4) * side * side     print ("Area of Equilateral Triangle: % f"% area)  # Function to calculate Perimeter # of equilateral triangle def perimeter( side ):     perimeter = 3 * side     print ("Perimeter of Equilateral Triangle: % f"% perimeter)      # Driver code side = 4 area_equilateral( side ) perimeter( side )
C# 
// C# Program to find area and // perimeter of equilateral triangle using System;  class GFG {     // Function to calculate     // Area of equilateral triangle     static float area_equi_triangle(float side)     {          return (float)(((Math.Sqrt(3)) / 4) *                         side * side);     }      // Function to calculate     // Perimeter of equilateral     // triangle     static float peri_equi_triangle(float side)     {         return 3 * side;     }          // Driver Code     public static void Main()     {         float side = 4;         Console.Write("Area of Equilateral Triangle:");         Console.WriteLine(area_equi_triangle(side));         Console.Write("Perimeter of Equilateral Triangle:");         Console.WriteLine(peri_equi_triangle(side));     } }  // This code is contributed // by vt_m.
PHP 
<?php // PHP program to find area // and perimeter of equilateral triangle   // Function to calculate Area // of equilateral triangle function area_equi_triangle( $side) {     return sqrt(3) / 4 * $side * $side; }  // Function to calculate Perimeter // of equilateral triangle function peri_equi_triangle( $side) {     return 3 * $side; }  // Driver Code  $side = 4; echo("Area of Equilateral Triangle: "); echo(area_equi_triangle($side)); echo("\n"); echo("Perimeter of Equilateral Triangle: "); echo( peri_equi_triangle($side));  // This code is contributed // by vt_m. ?>
JavaScript 
<script>     //Javascript program to find area     // and perimeter of equilateral triangle          // Function to calculate      // Area of equilateral triangle     function area_equi_triangle(side)     {         return (((Math.sqrt(3)) / 4) * side * side).toFixed(4);     }          // Function to calculate      // Perimeter of equilateral     // triangle     function peri_equi_triangle(side)     {         return 3 * side;     }          //Driver code     var side = 4;     document.write("Area of Equilateral Triangle:");     document.write(area_equi_triangle(side)+"\n");     document.write("Perimeter of Equilateral Triangle:");     document.write(peri_equi_triangle(side)+"\n");          //This code is contributed by shruti456rawal </script>

Output
Area of Equilateral Triangle: 6.9282  Perimeter of Equilateral Triangle: 12

Time Complexity: O(1)

Auxiliary Space: O(1)


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Minimum height of a triangle with given base and area

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    Find all the possible coordinates from the three coordinates to make a parallelogram of a non-zero area.Let's call A, B, and C are the three given points. We can have only the three possible situations:  (1) AB and AC are sides, and BC a diagonal(2) AB and BC are sides, and AC a diagonal (3) BC and
    5 min read
    Maximum area of quadrilateral
    Given four sides of quadrilateral a, b, c, d, find the maximum area of the quadrilateral possible from the given sides .Examples:  Input : 1 2 1 2Output : 2.00It is optimal to construct a rectangle for maximum area .  According to Bretschneider's formula, the area of a general quadrilateral is given
    5 min read
    Check whether four points make a parallelogram
    Given four points in a 2-dimensional space we need to find out whether they make a parallelogram or not. A parallelogram has four sides. Two opposite sides are parallel and are of same lengths. Examples:Points = [(0, 0), (4, 0), (1, 3), (5, 3)]Above points make a parallelogram.Points = [(0, 0), (2,
    15+ min read
    Find the Missing Point of Parallelogram
    Given three coordinate points A, B and C, find the missing point D such that ABCD can be a parallelogram.Examples : Input : A = (1, 0) B = (1, 1) C = (0, 1) Output : 0, 0 Explanation: The three input points form a unit square with the point (0, 0) Input : A = (5, 0) B = (1, 1) C = (2, 5) Output : 6,
    13 min read

    Problems based on Polygon and Convex Hull

    How to check if a given point lies inside or outside a polygon?
    Given a polygon and a point 'p', find if 'p' lies inside the polygon or not. The points lying on the border are considered inside. Examples: Recommended ProblemPlease solve it on PRACTICE first, before moving on to the solution Solve ProblemApproach: The idea to solve this problem is based on How to
    9 min read
    Area of a polygon with given n ordered vertices
    Given ordered coordinates of a polygon with n vertices. Find the area of the polygon. Here ordered means that the coordinates are given either in a clockwise manner or anticlockwise from the first vertex to last.Examples : Input : X[] = {0, 4, 4, 0}, Y[] = {0, 0, 4, 4}; Output : 16 Input : X[] = {0,
    6 min read
    Tangents between two Convex Polygons
    Given two convex polygons, we aim to identify the lower and upper tangents connecting them. As shown in the figure below, TRL and TLR represent the upper and lower tangents, respectively. Examples: Input: First Polygon : [[2, 2], [3, 3], [5, 2], [4, 0], [3, 1]] Second Polygon : [[-1, 0], [0, 1], [1,
    15 min read
    Find number of diagonals in n sided convex polygon
    Given n > 3, find number of diagonals in n sided convex polygon.According to Wikipedia, In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal.Examples : Input : 5Outp
    3 min read
    Convex Hull using Jarvis' Algorithm or Wrapping
    Given a set of points in the plane. the convex hull of the set is the smallest convex polygon that contains all the points of it.We strongly recommend to see the following post first. How to check if two given line segments intersect?The idea of Jarvis's Algorithm is simple, we start from the leftmo
    13 min read
    Convex Hull using Graham Scan
    A convex hull is the smallest convex polygon that contains a given set of points. It is a useful concept in computational geometry and has applications in various fields such as computer graphics, image processing, and collision detection.A convex polygon is a polygon in which all interior angles ar
    15+ min read
    Dynamic Convex hull | Adding Points to an Existing Convex Hull
    Given a convex hull, we need to add a given number of points to the convex hull and print the convex hull after every point addition. The points should be in anti-clockwise order after addition of every point. Examples: Input : Convex Hull : (0, 0), (3, -1), (4, 5), (-1, 4) Point to add : (100, 100)
    15 min read
    Deleting points from Convex Hull
    Given a fixed set of points. We need to find convex hull of given set. We also need to find convex hull when a point is removed from the set. Example: Initial Set of Points: (-2, 8) (-1, 2) (0, 1) (1, 0) (-3, 0) (-1, -9) (2, -6) (3, 0) (5, 3) (2, 5) Initial convex hull:- (-2, 8) (-3, 0) (-1, -9) (2,
    15+ min read
    Minimum area of a Polygon with three points given
    Given three points of a regular polygon(n > 3), find the minimum area of a regular polygon (all sides same) possible with the points given.Examples: Input : 0.00 0.00 1.00 1.00 0.00 1.00 Output : 1.00 By taking point (1.00, 0.00) square is formed of side 1.0 so area = 1.00 . One thing to note in
    13 min read
    Find Simple Closed Path for a given set of points
    Given a set of points, connect the dots without crossing. Example: Input: points[] = {(0, 3), (1, 1), (2, 2), (4, 4), (0, 0), (1, 2), (3, 1}, {3, 3}}; Output: Connecting points in following order would not cause any crossing {(0, 0), (3, 1), (1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (0, 3)} We strongl
    11 min read
    Minimum Distance between Two Points
    You are given an array arr[] of n distinct points in a 2D plane, where each point is represented by its (x, y) coordinates. Find the minimum Euclidean distance between two distinct points.Note: For two points A(px,qx) and B(py,qy) the distance Euclidean between them is:Distance = \sqrt{(p_{x}-q_{x})
    15+ min read
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