Question

The parallel sides of the trapezium are 10cm and 12cm and one of its non parallel side is 13cm. find the are of trapezium?

Answer 1

Solution:

Given:The parallel sides of the trapezium are 10cm and 12cm and one of its non parallel side is 13cm.

If we draw the diagram,
               10cm
B  ______________ C
    l                               l\
    l                               l  \   13cm
    l                            h l    \
    l_____________  l___\ D
A                                    E
                12cm
AE=BC (parallel to each other and so, equal)
AD=AE+ED
 12= 10+ED
  ED=2cm..

By applying pythagoras theorem,
we get,

h²+2²=13²
h²+4=169
     h²= 169-4
     h²=165
     h=√165
     h=12.85cm

Area of Trapezium = $\frac{1}{2} h(a+b) sq.units$
                                  =$\frac{1}{2} (12.85)(12+10)$
                                  =$6.425(22)$
                                  =141.35cm²