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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Answer 1

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...