Question

A field is in the shape of trapezium whose parallel sides are 20m and 10 m .The non-parallel sides are 13m and 13m . Find the area of the field​

Answer 1

Answer:

Step-by-step explanation:

Construction:  

⇒Draw BE∥AD such that D−E−C

⇒Draw BM⊥DC such that D−E−M−C

□ABED is parallelogram,

⇒AD=BE=13  m

⇒AB=DE=10  m

⇒BC=14  m

⇒DC=DE+EC   ....(∵D−E−C)

∴EC=25−10

∴EC=15  m

⇒In ΔBEC

⇒2S=13+14+15

⇒S=21  m

⇒Area of △BEC

⇒A=  

s(s−a)(s−b)(s−c)

​  

   

=  

21(21−13)(21−14)(21−15)

​  

 

=  

21×8×7×6

​  

 

=84  m  

2

 

⇒Area of ΔBCE=  

2

1

​  

×BM×EC

⇒BM=  

15

84×2

​  

 

             =11.2  cm

⇒Area of □ABED=11.2×10=112  m  

2

 

⇒Area of the field □ABCD

=84+112  m  

2

 

=196  m  

2