Interface

#include <codecogs/geometry/area/right_triangle.h>

using namespace Geometry::Area;

	double	right_triangle (double a, double b, double c, double h)[inline] Computes the area of a trapezium within a right angled triangle with a fixed edge.
	Real	cc_right_triangle (Real a, Real b, Real c, Real h) This function is available as a Microsoft Excel add-in.

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Function Documentation

This module computes the area of the trapezium formed between a right angled triangle with a fixed edge on a reference line and a line found at a given distance distance from this reference line.

This situation is described by the following image. The area which we want to compute is that of the filled trapezium .

Solution

Let be an orthogonal coordinate system and let be a right angled triangle () so that and

(1)

where are fixed numbers. Also let so that the distance from line to is and , .

Obviously , which implies:

(2)

Thus:

(3)

To conclude, the solution of the problem is:

(4)

Example:

#include <codecogs/geometry/area/right_triangle.h>
#include <stdio.h>
 
int main()
{
  // the lengths of the sides
  double a = 3.0, b = 4.0, c = 5.0;
 
  // display the lengths of the sides
  printf("a = %.1lf\nb = %.1lf\nc = %.1lf\n\n", a, b, c);
 
  // display the area for different values of h
  for (double h = 0.1; h < 1.09; h += 0.1)
    printf("h = %.1lf   Area = %.2lf\n", h, Geometry::Area::right_triangle(a, b, c, h));
 
  return 0;
}

Output:

a = 3.0
b = 4.0
c = 5.0
 
h = 0.1   Area = 0.30
h = 0.2   Area = 0.59
h = 0.3   Area = 0.87
h = 0.4   Area = 1.14
h = 0.5   Area = 1.41
h = 0.6   Area = 1.66
h = 0.7   Area = 1.92
h = 0.8   Area = 2.16
h = 0.9   Area = 2.40
h = 1.0   Area = 2.62

Parameters:

a	first side of the triangle (BC)
b	second side of the triangle (AC)
c	third side of the triangle (AB)
h	the distance between line and

Returns:

The value of the desired area.

Note:

The values of the sides must be Pythagorean numbers, i.e. satisfying the equality:

(5)

Authors:

Eduard Bentea (September 2006)

Source Code:

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