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# right triangle

Computes the area of a trapezium within a right angled triangle with a fixed edge.
Controller: CodeCogs

C++
Excel

## Right Triangle

 doubleright_triangle( double a double b double c double h )[inline]
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

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

Obviously , which implies:

Thus:

To conclude, the solution of the problem is:


### Example 1

#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

### Note

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


### 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 buy a Commercial licence.

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