2. 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 trapezi

Question

2. 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.

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2 months 2021-10-04T21:37:53+00:00 1 Answer 0 views 0

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    2021-10-04T21:39:04+00:00

    Answer:

    Step-by-step explanation:

    Draw CE such that AECD is a parallelogram

    AE = CD = 11 cm

    AD = CE = 15 cm

    EB = 14 cm

    Area of ΔECB = s(s-a)(s-b)(s-c)

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

    a = 13 cm, b = 14 cm, c = 15 cm

    Here s = (13+14+15)/2 = 21 cm

    Area of ΔECB = 21(21-13)(21-14)(21-15)

         

    = 84 sq cm

    But Area of ΔECB = 1/2 × base (EB) × height (h)

    1/2 × 14 × h = 84

    h = 12 cm

    Area of trapezium ABCD = 1/2 × h × (AB + CD)

     

                                            = 1/2 × 12 × (25 + 11)  

             

                                            =  6 × 36

     

                                            = 216 sq cm

    Hope it Helps…

     

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