A field is in the shape of trapezium whose Parrell sides are 10m and 26 m non parrerll sides are 18 m and 14m .Find the area

Question

A field is in the shape of trapezium
whose
Parrell sides are 10m and 26 m
non parrerll sides are 18 m and 14m .Find the area of the field . Value of
 \sqrt{5}

in progress 0
Katherine 2 weeks 2021-09-09T12:47:11+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-09T12:48:15+00:00

    Answer:

    nii pata mere ko iska formula laga ke dekha hai ki paka pakya hi khana hai

    0
    2021-09-09T12:49:06+00:00

    Figure is in the attachment

    _____________________________


    Given:

    AB || CD

    AB =25 m

    CD= 10m

    BC=14m

    AD= 13m


    From point C draw CE || DA . Hence ADCE is a ||grm having CD || AE & AD||CE


    AE= CD= 10m

    CE= AD= 13m

    BE= AB- AE =25- 10=15 m

    BE= 15m


    In ∆BCE

    BC= 14m, CE= 13m, BE= 15m


    Semiperimeter (s)= (a+b+c)/2


    Semiperimeter(s) =( 14+13+15)/2

    s= 42/2= 21m

    s= 21m


    Area of ∆BCE= √ s(s-a)(s-b)(s-c)

    Area of ∆BCE=√ 21(21-14)(21-13)(21-15)


    Area of ∆BCE= √ 21×7× 8×6


    Area of ∆BCE= √ 7×3× 7× 4×2×2×3

    Area of ∆BCE=√7×7×3×3×2×2×4

    Area of ∆BCE= 7×3×2×2= 21× 4= 84m²


    Area of ∆BCE= 84m²


    Area of ∆BCE= 1/2 × base × altitude

    Area of ∆BCE= 1/2 × BE ×CL


    84= 1/2×15×CL


    84×2= 15CL

    168= 15CL

    CL= 168/15

    CL= 56 /5m


    Height of trapezium= 56/ 5m


    Area of trapezium= 1/2( sum of || sides)( height)


    Area of trapezium=1/2(25+10)(56/5)

    Area of trapezium= 1/2(35)(56/5)


    Area of trapezium= 7×28= 196m²

    _____________________________

    Hence the area of field is 196m²

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