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# edge triangle

Computes the area of a trapezium within a triangle with a fixed edge.
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## Edge Triangle

 doubleedge_triangle( double a double b double c double h )[inline]
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 where are fixed numbers. Also let so that the distance between the line and equals and , .

Obviously which implies:

where H is the height corresponding to vertex A.

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### Example 1

#include <codecogs/maths/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

### Note

The values of the sides must satisfy the triangle inequality.

### 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.

### Authors

Eduard Bentea (September 2006)
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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