Question

. The parallel sides of a trapezium are 25 cm and 11 cm, while its non-parallel sides are 15 cm
and 13 cm. Find the area of the trapezium.​

Answer 1

Answer:

216sq cm

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