Question

two parallel sides of a trapezium are 60cm and 77cm and other sides are 25cm and 26cm. find the area of the trapezium.

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

bye :-)