Interface

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

using namespace Geometry::Area;

	double	edge_triangle (double a, double b, double c, double h)[inline] Computes the area of a trapezium within a triangle with a fixed edge.
	Real	cc_edge_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 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 an arbitrary triangle so that and

(1)

where are fixed numbers. Also let so that the distance between the line and equals and , .

Obviously which implies:

(2)

where H is the height corresponding to vertex A.

Further information available when you purchase a licence.

Example:

#include <codecogs/geometry/area/edge_triangle.h>
#include <stdio.h>
 
int main()
{
  // the lengths of the sides
  double a = 3.3, b = 4.5, c = 5.4;
 
  // 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::edge_triangle(a, b, c, h));
 
  return 0;
}

Output:

a = 3.3
b = 4.5
c = 5.4
 
h = 0.1   Area = 0.33
h = 0.2   Area = 0.65
h = 0.3   Area = 0.96
h = 0.4   Area = 1.26
h = 0.5   Area = 1.56
h = 0.6   Area = 1.85
h = 0.7   Area = 2.13
h = 0.8   Area = 2.40
h = 0.9   Area = 2.67
h = 1.0   Area = 2.93

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 satisfy the triangle inequality.

Authors:

Eduard Bentea (September 2006)

Source Code:

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