Question

WHAT WILL BE THE PERIMETER OF AN ISOSCELES TRAPEZIUM WHOSE PARALLEL SIDES ARE OF LENGTH 10 cm AND 20 cm RESPECTIVELY AND ONE OF THE NON PARALLEL SIDES IS 8 CM?

Answer 1

ANSWER

REF.Image.

In isosceles trapezium, AD = BC

Let DC = 3a cm

⇒ AB = a cm

As sum of opposite sides is equal,

⇒AD+BC=4a⇒2AD=4a⇒AD=2a

Now perimeter = 16 cm ⇒8a=16⇒a=2cm

In △ALD,AL

2

=AD

2

−DL

2

(Pythagoras th.)⇒AL

2

=16−4=12

⇒AL=

12

=2

3

cm

Now, Area of trapezium =

2

1

(Sum of parallel sides)Height

=

2

1

(4a)(2

3

)

=2a×2

3

=4×2

3

=8

3 cm

2

solution