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C++ Program to Find Area, Perimeter, and Side of a Rhombus

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C++ Program to Find Area, Perimeter, and Side of a Rhombus

C++ Program to Find Area, Perimeter, and Side of a Rhombus

Introduction

A rhombus is a type of quadrilateral where all four sides have equal lengths. It is commonly known as a diamond shape. In geometry, calculating properties such as the area, perimeter, and side length is crucial for understanding this figure. The diagonal lengths play a significant role in these calculations.

In this program, we will create a C++ code to calculate the area, perimeter, and the side length of a rhombus using the lengths of its diagonals.

Formulas

To perform the calculations for a rhombus, we use the following formulas:

  • Area: The area of a rhombus can be calculated using its diagonals (d1 and d2). The formula is: Area = (d1 × d2) / 2.
  • Perimeter: The perimeter is the sum of all the sides of the rhombus. Since all sides are equal, the formula becomes: Perimeter = 4 × side.
  • Side Length: Using the Pythagorean theorem, we can determine the length of a side when the diagonals are known: Side = √((d1/2)² + (d2/2)²).

Code

Below is the C++ program to calculate the area, perimeter, and side length of a rhombus: 

#include <iostream>
#include <cmath>

using namespace std;

int main() {
    // Variables to store the lengths of diagonals
    double d1, d2;

    // Input the diagonals
    cout << "Enter the length of the first diagonal (d1): ";
    cin >> d1;

    cout << "Enter the length of the second diagonal (d2): ";
    cin >> d2;

    // Calculate the area of the rhombus
    double area = (d1 * d2) / 2;

    // Calculate the side length of the rhombus
    double half_d1 = d1 / 2;
    double half_d2 = d2 / 2;
    double side = sqrt((half_d1 * half_d1) + (half_d2 * half_d2));

    // Calculate the perimeter of the rhombus
    double perimeter = 4 * side;

    // Display the results
    cout << "Area of the rhombus: " << area << " square units" << endl;
    cout << "Side length of the rhombus: " << side << " units" << endl;
    cout << "Perimeter of the rhombus: " << perimeter << " units" << endl;

    return 0;
}

Output

Here is an example of how the program works with sample inputs: 

Enter the length of the first diagonal (d1): 10
Enter the length of the second diagonal (d2): 8
Area of the rhombus: 40 square units
Side length of the rhombus: 6.40312 units
Perimeter of the rhombus: 25.6125 units

Explanation

The program begins by taking the lengths of the two diagonals (d1 and d2) as input from the user. These values are used to calculate:

  • Area: The diagonals are multiplied and divided by 2 to compute the area.
  • Side Length: Each diagonal is halved, and the Pythagorean theorem is applied to find the side length of the rhombus.
  • Perimeter: The side length is multiplied by 4 to calculate the total perimeter.

The results are displayed to the user, providing a clear understanding of the rhombus's geometric properties.

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