Question

a field is in the shape of trapezium whose parallel sides are 35 and 15 the non parallel sides are 16 and 18 find the area of the field ​

Answer 1

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= root of √s(s−a)(s−b)(s−c)

__________________

= √21(21−13)(21−14)(21−15)

_________

= √21×8×7×6

=84 m ^2

⇒Area of ΔBCE= 1/2×BM×EC

⇒BM= (84×2)/15=11.2 cm

⇒Area of □ABED=11.2×10=112 m ^2

⇒Area of the field □ABCD

=84+112 m ^2

=196 m ^2

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