Question

,菱形周长为2p,两条对角线的和为m,求菱形面积.

Answer 1

设菱形的两条对角线长度分别为x、y,则可知菱形面积

S = (xy)/2

由勾股定理可知：

(x/2)^2 + (y/2)^2 = (2p/4)^2

化简得：x^2 + y^2 = p^2

又因为：x + y = m

所以：

S = (xy)/2 = (1/2)*{[(x+y)^2 - (x^2 + y^2)]/2}

=(1/4)(m^2 - p^2)