Area of the largest triangle that can be inscribed within a rectangle?

A rectangle is a quadrilateral that has opposite sides equal and parallel, with adjacent sides at 90°. A triangle is a closed figure with three sides.

The largest triangle that can be inscribed within a rectangle has its base equal to the length of the rectangle and height equal to the breadth of the rectangle. This triangle spans the entire diagonal of the rectangle.

Syntax

Area = (1/2) × length × breadth

Example

Here's a program to calculate the area of the largest triangle inscribed in a rectangle −

#include <stdio.h>

int main() {
    int length = 10, breadth = 9;
    float area;
    
    /* Calculate area using the formula: (1/2) * length * breadth */
    area = (float)(length * breadth) / 2.0;
    
    printf("Rectangle dimensions: Length = %d, Breadth = %d<br>", length, breadth);
    printf("Area of largest triangle inscribed = %.2f<br>", area);
    
    return 0;
}

Rectangle dimensions: Length = 10, Breadth = 9
Area of largest triangle inscribed = 45.00

Key Points

• The largest inscribed triangle always has one vertex at a corner and the opposite side along the diagonal of the rectangle.
• The area formula is exactly half the area of the rectangle: Area = (1/2) × l × b
• This triangle occupies exactly 50% of the rectangle's area.

Conclusion

The largest triangle inscribed in a rectangle has an area equal to half the rectangle's area. The formula (1/2) × length × breadth provides a simple calculation for this geometric problem.