Question

Parallel sides of a trapezium are 40m and 100m. The non-parallel sides are 52m and 56m respectively. Which of the following is the area of the trapezium(in m^2)​

Answer 1

Answer:

Draw a line BC parallel to AD

Draw a perpendicular line BE on DF

ABCD is a parallelogram.

BC=AD=25 cm

CD=AB=60 cm

CF=77−CD=17cm

For ΔBCF

semiperimeter of triangle=

2

25+26+17

=

2

68

=34

By Heron's Formula of triangle=

s(s−a)(s−b)(s−c)

=

34(34−25)(34−26)(34−17

)

=204cm²

Also, area of ΔBCF=

2

1

×base×height

204=

2

1

BE×CF

204=

2

1

BE×17

BE=408/17

BE=24 cm

Area of Trapezium=

2

1

(AB+DF)×BE

=1/2(60+77)×24

Area=1644cm²