Subject: Optional Maths
∴ \(\square\)ABCD = ½\(\begin{vmatrix}x_1&x_2&x_3&x_1\\y_1&y_2&y_3&y_1 \end{vmatrix}\) + ½ \(\begin{vmatrix}x_1&x_3&x_4&x_1\\y_1&y_3&y_4&y_1 \end{vmatrix}\)
_x000D_=½ (x1 y2-x2 y1+x2 y3-x3 y2+x3 y1-x1 y3) +½ (x1 y3-x3 y1+x3 y4-x4 y3+x4 y1-x1 y4)
_x000D_=½ (x1y2-x2y1+x2y3-x3y2+x3y4-x4y3+x4y1-x1y4)
_x000D_Note : To find the area of a quadrilateral by using this formula, the vertices of quadrilateral should be taken in order. So it is better to plot the points roughty before applying the formula. Otherwise the result may be wrong.
_x000D_Note: To find the area of a quadrilateral, we divide it into two triangles by joining a diagonal. Then the sum of the areas of the two triangles will be equal to the area of the quadrilateral.
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