Question

find the area of trapezium whose parallel sides are 25m and 13 m. the non parallel sides are 15 m and 15 m...? [by herons formula] please solve it??.... ​

Answer 1

Answer:

Step-by-step explanation:

Trapezium ABCD is divide into parallelogram AECD and triangle CEB.  

Now in △CEB, we have

EB=25−11=14cm

Using Heron’s theorem, we will first evaluate the semi-perimeter of △CEB and then evaluate its area.

S=  

2

BE+EC+BC

​  

 

⇒S=  

2

13+14+15

​  

=21cm

Therefore,

area of △CEB=  

S(S−BE)(S−EC)(S−BC)

​  

 

⇒ Area of △CEB=  

21(21−13)(21−14)(21−15)

​  

=84cm  

2

 

As we know that,

Area of triangle =  

2

1

​  

× Base × height

Therefore,

Area of △CEB=  

2

1

​  

×14×BF

⇒BF=  

14

84×2

​  

=12cm

Again, as we know that,

Area of trapezium = Sum of parallel sides × height

Therefore,

Area of trapezium ABCD=  

2

1

​  

×(11+25)×12=216cm  

2

 

Thus the area of trapezium is 216cm  

2

.

Hope It helps u