Question

7. Find the area of the parallelogram ABCD in
which AB= 14 cm, BC = 10 cm,
AC =16 cm. Take 3 =173.​

Answer 1

Answer

In ΔABC

Take a = 10cm, b = 16cm and c = 14cm

So we get  s=  2  a+b+c

s=  2  10+16+14

By division

s=20cm

We know that

Area=  s(s−a)(s−b)(s−c)

​By substituting the values

Area=  20(20−10)(20−16)(20−14)

So we get

Area=  10×2×10×4×3×2

​It can be written as  

Area=  10×10×4×2×2×3

​  

 

On further calculation

Area=10×2×2× 3

​  

 

So we get

Area=14×3×4×2

By multiplication

Area=40  

​  

 

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

So we get  

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(40 ) __-.... 3

​  

So we get

Area of parallelogram ABCD=80 .... 3

​  

 

By substituting   3

​  

 

Area of parallelogram ABCD = 80(1.73)

So we get  

Area of parallelogram ABCD =138.4cm  

Therefore, the area of parallelogram ABCD is 138.4cm