Question

The sum of parallel sides of a trapezium is 58cm. If the perpendicular distance between the parallel sides is 4cm, the area of the trapezium is a) 58 sq. cm b) 116 sq. cm c) 116 cm d) 29 sq. cm​

Answer 1

Step-by-step explanation:

Let the two parallel sides of the trapezium be a cm and b cm.

Given that difference between the two parallel sides is 4 and the perpendicular distance(h) is 19

⇒a−b=4⟶(1)

We know that Area of Trapezium =

2

1

×(a+b)×h

Substituting the values of h we get,

2

1

×(a+b)×19=475

⇒(a+b)=

19

475×2

⇒a+b=50⟶(2)

Adding (1) and (2),

a−b=4

a+b=50

−2b=−54

b=

2

54

=27

Putting b=27 in (2) we get

a+27=50

a=50−27=23

Two parallel sides are 27 cm and 23 cm.

Answer 2

Step-by-step explanation:

Perimeter =52cm

a+b+10+10=52

a+b=32cm

h=8cm

Area =

2

1

(a+b)×h

Area =

2

1

×32×8=128cm

2