Question

a field is in the shape of a trapezium whose parallel sides are 25m and 10m the non parallel sides are 14 and 13 metre find the area of the field.​

Answer 1

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=(a+b+c) /2

s= (14+13+15) /2

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= 1/2 ×base×height

84= 1/2 ×15×CL

(84×2) /15=CL

CL= 56/5m

Now, the area of trapezium is,

A= 1/2(sumofparallelsides)(height)

A= 1/2×(25+10)( 56/5)

A=196m^2

Therefore, the area of the trapezium is 196m ^2

Answer 2

Answer:

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