Question

A field in the shape of trapezium whose parallel sedes are 25 m and 10m and non parellel sides are 14 and 13 find the area of the field

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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=√s(s−a)(s−b)(s−c)

= √21(21−13)(21−14)(21−15)

= √21×8×7×6

=84 m²

⇒Area of ΔBCE= 1/2×BM×EC

⇒BM= 84×2/15

=11.2 cm

⇒Area of □ABED=11.2×10=112 m²

⇒Area of the field □ABCD

=84+112 m²

=196 m²

Step-by-step explanation:

Hope this answer will be helpful..

Answer 2

Step-by-step explanation:

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 = 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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