I have forgotten
my Password

Or login with:

  • Facebookhttp://facebook.com/
  • Googlehttps://www.google.com/accounts/o8/id
  • Yahoohttps://me.yahoo.com
get GPL
COST (GBP)
this unit 4.50
sub units 0.00
+
0
MathsGeometryArea

edge triangle

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

get GPL add to cart

Interface

C++
HTML

Edge Triangle

 
doubleedge_triangledoublea
doubleb
doublec
doubleh )[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 [BB_1C_1C].

1/edge_triangle-746.jpg
+

Solution

Let \mathrm{xOy} be an orthogonal coordinate system and let \triangle ABC be an arbitrary triangle so that BC \subset \mathrm{Ox} and where a, b, c \in \mathbb{R}_+^* are fixed numbers. Also let d  \parallel \mathrm{Ox} so that the distance between the line d and \mathrm{Ox} equals h \in \mathbb{R}_+ and AB \cap d = \{B_1\}, AC \cap d = \{C_1\}.

Obviously \triangle AB_1C_1 \sim \triangle ABC which implies:

where H is the height corresponding to vertex A.

Purchase a Licence for more information.

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

afirst side of the triangle (BC)
bsecond side of the triangle (AC)
cthird side of the triangle (AB)
hthe distance between line d and \mathrm{Ox}

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.

Not a member, then Register with CodeCogs. Already a Member, then Login.