- Trending Categories
Data Structure
Networking
RDBMS
Operating System
Java
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
C++ program to find the Area of the Largest Triangle inscribed in a Hexagon?
Find the area of largest Triangle inscribed in a hexagon we need to learn these figures are and how 1 is inscribed inside other.
Triangle is a closed figure with 3 sides which may be equal or different size.
Hexagon is a closed figure with 6 sides which may be equal or unequal in size.
A triangle inscribed inside a hexagon has all its vertices touching vertices of hexagon. So, the sides of the triangle can be treated as diagonals of a regular hexagon. The hexagon considered here is a regular hexagon, which leads to make the largest triangle an Equilateral triangle.
Let’s derive the formula for this,
Please refer to the following image −
In triangle AGB, we apply pythagoras theorem.
(a/2)2 + (s/2)2 = a2 ,a = side of regular hexagon
s = side of equilateral triangle
a2/4 + s2/4 = a2
a2 - a2/4 = s2/4 3a2/4 = s2/4 3a2 = s2 a√3 = s Area = (3√3*a^2)/4
Let’s take an example,
Side of hexagon = 6
Area of triangle = 46.7654
Explanation, Area = 3√3*36/4 = 46.7654
Example
#include <iostream> #include <math.h> using namespace std; int main() { float a = 6; if (a < 0) cout<<"Wrong Input!"; float area = (3 * sqrt(3) * pow(a, 2)) / 4; cout <<"The area of the triangle is "<<area; return 0; }
Output
The area of the triangle is 46.7654
- Related Articles
- Area of the Largest Triangle inscribed in a Hexagon in C++
- Area of largest triangle that can be inscribed within a rectangle in C Program?
- Area of a square inscribed in a circle which is inscribed in a hexagon in C Program?
- C Program for Area of a square inscribed in a circle which is inscribed in a hexagon?
- Find the area of largest circle inscribed in ellipse in C++
- Area of the largest triangle that can be inscribed within a rectangle?
- Area of a circle inscribed in a regular hexagon?
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon in C?
- Area of a triangle inscribed in a rectangle which is inscribed in an ellipse In C Program?
- ( A B C D E F ) is a regular hexagon with centre ( O ). If the area of triangle ( O A B ) is 9 ( mathrm{cm}^{2} ), find the area of the circle in which the hexagon is inscribed."\n
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle in C Program?
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle in C Program?
- A regular hexagon is inscribed in a circle. If the area of hexagon is ( 24 sqrt{3} mathrm{~cm}^{2} ), find the area of the circle. (Use ( pi=3.14 ) )
- Find the area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units, in square units.
- Area of largest Circle inscribed in N-sided Regular polygon in C Program?
