Question

the area of a Trapezium whose parallel sides are 25 m and 10 M and the non parallel sides are 14m and 13m

Answer 1

Let ABCD is a trapezium such that AB = 25m, BC = 13 m, CD = 10 m and DA = 14 m 
Draw a line DE parallel to the side BC =13 m therefore DE = 13 m 
AE+ED+DA = 15+13+14 = 42 
2s= 42 or s = 21 
Area of triangle DAE using Hero's formula = sqrt{ 21(21-15)(21-14)(21-13)} = 84 m^2............(i) 
DF is a perpendicular from D on AE= h 
Area of triangle = (1/2)(15)(h)............................... 
from (i) and (ii) 
(15/2)*h = 84 
h = (84*2)/15 = 11.2 m...................................(iii... 
Area of parallelogram = 10*11.2 = 112 m^2...........................(iv) 
Therefore area of trapezium = Area of triangle+ Area of parallelogram 
= 84 +112 = 196 m^2..............................Ans