Area of the biggest possible rhombus that can be inscribed in a rectangle in C Program?

Here we will see one problem, where one rectangle is given. We have to find the area of largest rhombus that can be inscribed in the rectangle.

The length of the rectangle is 'l' and breadth is 'b'. The largest rhombus that can be inscribed in a rectangle has its diagonals equal to the length and breadth of the rectangle.

Syntax

Area of rhombus = (diagonal1 × diagonal2) / 2
Area = (l × b) / 2

Example

Here's a C program to calculate the area of the largest rhombus that can be inscribed in a rectangle −

#include <stdio.h>

float calculateRhombusArea(float length, float breadth) {
    if (length < 0 || breadth < 0) {
        return -1; /* Invalid input */
    }
    return (length * breadth) / 2.0;
}

int main() {
    float l = 20.0, b = 7.0;
    float area = calculateRhombusArea(l, b);
    
    if (area == -1) {
        printf("Invalid dimensions!<br>");
    } else {
        printf("Rectangle dimensions: Length = %.1f, Breadth = %.1f<br>", l, b);
        printf("Area of largest inscribed rhombus: %.1f<br>", area);
    }
    
    return 0;
}

Rectangle dimensions: Length = 20.0, Breadth = 7.0
Area of largest inscribed rhombus: 70.0

How It Works

The largest rhombus that can be inscribed in a rectangle has its vertices touching the midpoints of the rectangle's sides. The diagonals of this rhombus are equal to the length and breadth of the rectangle, making the area calculation straightforward using the rhombus area formula.

Conclusion

The area of the largest rhombus inscribed in a rectangle is simply half the product of the rectangle's dimensions. This geometric relationship makes the calculation efficient and straightforward.