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中学数学实际上计算了两种凸四边形(平行四边形和梯形)的面积。对于不是平行四边形或梯形的四边形,没有推导出它的面积公式。因此,我们来考虑任意凸四边形面积的计算公式,如果考虑到其某种外形相似处,那么可以把这个公式叫做海伦公式的类似公式。定理:任意凸四边形面积可按照下列公式确定: S=A-abcd 2cos~2δ+β/(1/2)其中A=(p-a)(p-b)(p-c)(p-d),a,b,c,d是边长,p是半周长,δ和β是四边形的对角。证明设在四边
High school math actually calculates the area of two convex quadrilaterals (parallelograms and trapezoids). For quadrilaterals that are not parallelograms or trapezoids, its area formula is not derived. Therefore, we consider the formula for calculating the area of any convex quadrilateral. If we consider a certain similarity of its shape, we can call this formula a similar formula of Helen’s formula. Theorem: The area of an arbitrary convex quadrilateral can be determined according to the following formula: S=A-abcd 2cos~2δ+β/(1/2) where A=(pa)(pb)(pc)(pd),a,b,c, d is the side length, p is the semi-circumference, and δ and β are diagonals of the quadrilateral. The proof is on the four sides