Question

Prove that that area of rhombus is equal to half of the product of diagnols

Answer 1

Answer:

Step-by-step explanation:

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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 = DB�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 = 2�(Area of triangle ABD)

So area of rhombus ABCD = 2�(DB�AE/2) = DB�AE

AE = AC/2 because the diagonals of a rhombus are perpendicular

bisectors of each other.

So area of rhombus DB�AE = DB�(AC/2) = DB�AC/2