Grade 108 grade maths

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

Smitha

8 Years agoGrade 10

1 Answer

Arun

8 Years ago

Draw CE such that AECD is a parallelogram
AE = CD = 11 cm
AD = CE = 15 cm

EB = 14 cm
Area of ΔECB = $\sqrt$ 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 = $\large \sqrt$ 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