Question

On the shape of a trapezium whose parallel sides are 25m and 10m the non parallel sides are 14m and 13m Find the area of the field​

Answer 1

Answer:

196msquare

Step-by-step explanation:

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

.