Question

Find area of trapezium if parallel sides are 22 m and 10 m and non parallel sides are 13 m and 14 m​

Answer 1

Answer:

Let ABCD be a trapezium with,

AB∥CD

AB=25m

CD=10m

BC=14m

AD=13m

Draw CE∥DA. So, ADCE is a parallelogram with,

CD=AE=10m

CE=AD=13m

BE=AB−AE=25−10=15m

In ΔBCE, the semi perimeter will be,

s=  

2

a+b+c

​  

 

s=  

2

14+13+15

​  

 

s=21m

Area of ΔBCE,

A=  

s(s−a)(s−b)(s−c)

​  

 

=  

21(21−14)(21−13)(21−15)

​  

 

=  

21(7)(8)(6)

​  

 

=  

7056

​  

 

=84m  

2

 

Also, area of ΔBCE is,

A=  

2

1

​  

×base×height

84=  

2

1

​  

×15×CL

15

84×2

​  

=CL

CL=  

5

56

​  

m

Now, the area of trapezium is,

A=  

2

1

​  

(sumofparallelsides)(height)

A=  

2

1

​  

×(25+10)(  

5

56

​  

)

A=196m  

2

 

Therefore, the area of the trapezium is 196m  

2

Step-by-step explanation: