Question

prove that the area of a rhombus is equal to half of the product of the diagonals

Answer 1

In the above figure d1,d2d1,d2 are the lengths of the diagonals.The area of rhombus ABCD = the area of triangle ABD + area of triangle BCD.Area ABCD = (1/2)∗(d2)∗(d1)/2+(1/2)∗(d2)∗(d1)/2(1/2)∗(d2)∗(d1)/2+(1/2)∗(d2)∗(d1)/2Area ABCD = (1/4)∗(d1)∗(d2)+(1/4)∗(d1)∗(d2)(1/4)∗(d1)∗(d2)+(1/4)∗(d1)∗(d2)Area ABCD = (1/2)∗(d1)∗(d2)