Question

Prove the area of Rhombus is equal to 1 divided by 2 X D1 X D2

Answer 1

from triangle AOB
area=1/2×b×h
=>1/2×OB×OA
=>1/2×AC/2×BD/2 (AC=BD & OB=1/2AC & OA=1/2BD)
ALL TRIANGLES ARE EQUAL
AOB=AOD=DOC=BOC
area of rhombus=area of (aob+aod+doc+boc)
=>ac×bd/8 + ac×bd/8 + ac×bd/8 + ac×bd/8
=>4(ac×bd)/8 (4×2=8)
=>ac×bd/2
=>1/2×ac×bd (ac and bd are diagonals)
=>1/2×d1×d2
HENCE PROVED

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Answer 2

Area of rhombus=2 × Area of triangle

ABC

$= 2 \times ( \frac{1}{2} \times d1 \times \frac{d2}{2} )$

So, Area of rhombus is

$\frac{1}{2} \times d1 \times d2 \: sq \: units$