The area of a triangle ABC can be calculated by |r_AB times r_AC|/2, where r_AB

Question

The area of a triangle ABC can be calculated by |r_AB times r_AC|/2, where r_AB and r_AC are vectors connecting the vertices A and B, and A and C, respectively. Determine the area of the triangle shown in the figure. Use the following steps in a script file to calculate the area. First, define the vectors r_OA, r_OB, and r_OC from knowing the coordinates of points A, B, and C. Then determine the vectors r_AB and r_AC from r_OA, r_OB, and r_OC. Finally, determine the area by using MATLAB's built-in functions cross, sum, and squareroot .

Explanation / Answer

r_OA = [8 5 -4];
r_OB = [-7 9 6];
r_OC = [-5 -2 11];
r_AB = r_OB - r_OA;
r_AC = r_OC - r_OA;
r_cross = cross(r_AB, r_AC);
area = sqrt(sum(r_cross.*r_cross))/2;
disp(area);

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