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Question -

If ABCD is a parallelogram, then prove that
ar (ΔABD) = ar (ΔBCD) = ar (ΔABC) = ar (ΔACD) = 1212 ar (||gm ABCD)




Answer -

Given: Here in the question it is given that
(1) ABCD is a Parallelogram
To Prove :
(1)  
(2)  
(3)  
(4)  
Construction: Draw  
Calculation: We know that formula for calculating the
Area of Parallelogram = base × height
Area of paralleogram ABCD = BC × AE (Taking base as BC and Height as AE ……(1)
We know that formula for calculating the
 
Area of ΔADC =  Base × Height
 (AD is the base of ΔADC and AE is the height of ΔADC)
=  Area of Parallelogram ABCD (from equation1)
 
Hence we get the result  
Similarly we can show that 
(2)  
(3)  
(4)  

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