Question

two parallel sides of a trapezium are 7 cm and 13 cm respectively and non parallel sides measures 5cm each. Then the area of trapezium is​

Answer 1

Answer:

Given AB=13 cm,CD=23 cm,AC=BD=10 cm each

construction Draw AP⊥CD & BQ⊥CD

Formulae:(i)Area of a trapezium =

2

1

×15 cm of parallel sides)×(perpendicular distance between then)

(ii) Pythagoras theorem

In quad ABPQ

AB∥PQ

AP∥BQ & AP=BQ{parallel lines} - (1)

In △APC & △BQD

∠APC=∠BQD=90

o

{construction}

AC=BD=10 cm= given

AP=BQ {from (1)}

∴ By RHS rule of congruence, △APC≅△BQD

Now let PC=QD=x

⇒2x+PQ=CD

2x=23−13=10 cm⇒x=5 cm

In △APC & △BQD

AP & BQ=

(10)

2

−(5)

2

=5

3

cm {Pythagoras Theorem}

Now area of Trapezium ABCD

=

2

1

×(AB+CD)×AP

=

2

1

×(13+23)×5

3

cm

2

=

2

1

×36×5

3

cm

2

=90

3

cm

2