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prove that area of rhombus is half of product of its diagonal.

Asked by shubham deshpande 6th January 2012, 8:55 PM
Answered by Expert
Answer:

Area of rhombus ABCD = area of triangle ABD + area of triangle CBD Triangles ABD and CBD are congruent by SSS

Area of rhombus ABCD = 2(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 = DBAE/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 = 2(Area of triangle ABD)
So area of rhombus ABCD = 2(DBAE/2) = DBAE AE = AC/2 because the diagonals of a rhombus are perpendicular bisectors of each other.
So area of rhombus DBAE = DB(AC/2) = DBAC/2
Answered by Expert 6th January 2012, 11:52 PM
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