Question
Thu March 03, 2011 By: Ayush Kumar

prove that area of a rhombus is half the area of its diagonals

Wed March 02, 2011
Dear Student,
Area of rhombus ABCD = area of triangle ABD + area of triangle CBD
Triangles ABD and CBD are congruent by SSS
Area of rhombus ABCD = 2ÃƒÂ—(Area of triangle ABD)
AE is perpendicular to DB because the diagonals of a rhombus are perpendicular bisectors of each other.
Area of triangle ABD = DBÃƒÂ—AE/2 because a triangle's area is one-half the product of a side and the altitude drawn to that side.
Area of rhombus ABCD = 2ÃƒÂ—(Area of triangle ABD)
So area of rhombus ABCD = 2ÃƒÂ—(DBÃƒÂ—AE/2) = DBÃƒÂ—AE
AE = AC/2 because the diagonals of a rhombus are perpendicular bisectors of each other.
So area of rhombus DBÃƒÂ—AE = DBÃƒÂ—(AC/2) = DBÃƒÂ—AC/2
Hence area of a rhombus is half the area of its diagonals
Regards
Team Topperlearning
Related Questions
Sat May 27, 2017

ABCD isa square. E,F,G,H are the midpoints of AB,BC,CD,DA respectively. Such that AE=CG=DH. Prove that EFGH is a square?

Sun January 08, 2017

Home Work Help