Question

Find the height of a trapezium in which parallel sides are 25 cm 77 cm and non-parallel sides and 26 cm and 60 cm. Given the area of the trapezium as 1644 sq.cm.

Answer 1

Hello,

let's look at the figure.

AB=60 cm;DF=77cm;AD=25cm; BF=26cmwe calculate the CF:

CF=DF-CD=77-60=17 cm

For ΔBCF,

we calculate the perimeter of triangle

P=BC+BF+CF=25+26+17=68 cm

we calculate the  semiperimeter of the triangle:

p=P/2=68/2=34 cm

we use the formula of Heron:

At=√p×(p-BC)×(p-BF)×(p-CF);

=√34(34-25)(34-26)(34-17)

=√34×9×8×17=√41616= 204 cm²

we calculate the height of triangle:

BE=2At:CF=(2×204):17=408:17=24 cm

we calculate the area of Trapezium

A =[(AB+DF)×BE):2=[(60+77)×24]=(137×24):2=3288:2=1644 cm²