Question

ABCD is a parallelogram de ab and df bc .if ab= 30cm, de=80cm and df=12cm . find bc?

Answer 1

Step-by-step explanation:

Solution

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In ΔABC

Take a = 26cm, b = 30cm and c = 28cm

So we get

s=  

2

a+b+c

​

 

s=  

2

26+30+28

​

 

By division

s=42cm

We know that

Area=  

s(s−a)(s−b)(s−c)

​

 

By substituting the values

Area=  

42(42−26)(42−30)(42−28)

​

 

So we get

Area=  

42×16×12×14

​

 

It can be written as  

Area=  

14×3×16×4×3×14

​

 

On further calculation

Area=  

14×14×3×3×16×4

​

 

So we get

Area=14×3×4×2

By multiplication

Area=336cm  

2

 

We know that the diagonal divides the parallelogram into two equal area  

So the area of parallelogram ABCD=Area of Δ ABC+Area of ΔACD

It can be written as

Area of parallelogram ABCD=2(Area of ΔABC)

By substituting the values  

Area of parallelogram ABCD=2(336)

By multiplication  

Area of parallelogram ABCD=672cm  

2

 

Therefore, the area of parallelogram ABCD is 672cm  

2