Question

The parallel sides of a trapezium are 25 cm and 11 cm, while its nonparallel sides are 15 cm and 13 cm. Find the area of the trapezium.
(Without Heron’s formula)

Answer 1

S=

2

AE+DE+DA

=

2

(25−11)+13+15

=

2

42

=21

Now Area of triangle =

s(s−a)(s−b)(s−c)

=

21(21−15)(21−14)(21−13)

=84 cm

2

Now draw DF ⊥ to E hence →

Area of △ADE=

2

1

× Base × height

84 cm

2

=

2

1

×14×h

h=12 cm

Now area of parallelogram =11×12=132 cm

2

Area of Trapezium =216 cm

2

{i.e,132+84}

Answer 2

first divide downside line then

make it 11

so both sides be right angled traingle

now Pythagorian triplet

so it becomes 15,9,12

then second side becomes 13,5,12

now downside length is divided so 14 remain

so it downside length is divided into 9,11,5

so it becomes 25

now add all side of right angled traingle

so, one side becomes 15+9+12=36

other side becomes 13+5+12=30

now area of rectangle l×b

so 11×12 =132

now add all 132+30+36= 198

area of trapezium is 198

hope my answer is correct