# right triangle

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

Controller: **CodeCogs**

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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