Question

A field is in the shape of a trapezium whose parallel sides are 25cm and 10cm .The non-parallel sides are 14cm and 13cm. find the area of the field.
​

Answer 1

Answer:

ANSWER

Construction:

⇒Draw BE∥AD such that D−E−C

⇒Draw BM⊥DC such that D−E−M−C

□ABED is parallelogram,

⇒AD=BE=13 m

⇒AB=DE=10 m

⇒BC=14 m

⇒DC=DE+EC ....(∵D−E−C)

∴EC=25−10

∴EC=15 m

⇒In ΔBEC

⇒2S=13+14+15

⇒S=21 m

⇒Area of △BEC

⇒A=

s(s−a)(s−b)(s−c)

=

21(21−13)(21−14)(21−15)

=

21×8×7×6

=84 m

2

⇒Area of ΔBCE=

2

1

×BM×EC

⇒BM=

15

84×2

=11.2 cm

⇒Area of □ABED=11.2×10=112 m

2

⇒Area of the field □ABCD

=84+112 m

2

=196 m

2

solution