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Calculating Areas With Triangulation If your triangles are not right angled, then what? You have to do the calculation for area in two steps. First find the coefficient of the triangle, we'll call it S. S= 1/2 (a + b +c) Then find the area A ___________________ A= √S x (S-a) x (S-b) x (S-c) You could set this up in a spread sheet to do the area of a property with straight sides, with length of each side known. Example: I have a triangle with sides measuring 5, 8, and 12 S = 1/2 * (5 + 8 + 12) = 12.5 _____________________________ A = √12.5 x (12.5-5) x (12.5-8) x 12.5-12) _________________ A = √12.5 x 7.5 x 4.5 x 0.5 _______ A = √210.9375 A = 14.5237 square units or it's 1/2 the two known sides times the sine of the interior angle of the two known sides. To find the length of an unknown side "a", two sides known and their interior angle (α) is known it's: __________________ a = √ b2 + c2 - 2bc x COS(α) Picture a property boundary with given sides and interior angles. You might divide the property into triangles as indicated with the dashed lines. Some interior angles may need to be measured with a protractor and some sides may need to be calculated. The math for these calculations is given above. In this case, the side that makes a long diagonal is calculated first so it can be used to find the length of the other diagonal of the next triangle to the left (middle) and it’s subsequent area. Where: __________________ a = √ b2 + c2 - 2bc x COS(α) ___________________________ a = √ 162 + 172 – 2 x 16 x 17x COS(91) ___________________________ a = √ 256 + 289 – 2 x 16 x 17x COS(91) ______ a = √ 554.49 a = 23.54 , note it’s not 32.95 as in the drawing. So find Area: S = ½ (a + b +c) = ½ (23.54 + 16 + 17) = 28.27 ___________________ A= √S x (S-a) x (S-b) x (S-c) ______________________________________ A= √28.27 x (28.27-23.54) x (28.27-16) x (28.27-17) ______________________ A= √28.27 x 4.73 x 12.27 x 11.27 _________ A= √18490.788 A= 135.98 square units. Continue on and the total area of all the triangles should be 247.36 square units.
