Question

Find the area of a trapezium whose parallel sides measure 60cm and 77cm and non-parallel sides are 25cm and 26cm.

Answer 1

Draw a line BC parallel to AD 

Draw a perpendicular line BE on DF

ABCD is a parallelogram.

BC=AD=25cm

CD=AB=60cm

CF=77-CD=17cm

For Δ BCF

perimeter of triangle=(25+26+17)/2

=68/2=34

By Heron's Formula of triangle=√s(s-a)(s-b)(s-c)

=√34(34-25)(34-26)(34-17)

=204cm²

Now area of ΔBCF=1/2xbase x height

=1/2 BExCF204cm²

=1/2x BEx17BE

=408/17

=24cm

Area of Trapezium =1/2(AB+DF)xBE

=1/2(60+77)x24

=1644cm²

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Answer 2

Answer:

Draw a line BC parallel to AD  

Draw a perpendicular line BE on DF

ABCD is a parallelogram.

BC=AD=25cm

CD=AB=60cm

CF=77-CD=17cm

For Δ BCF

perimeter of triangle=(25+26+17)/2

=68/2=34

By Heron's Formula of triangle=√s(s-a)(s-b)(s-c)

=√34(34-25)(34-26)(34-17)

=204cm²

Now area of ΔBCF=1/2xbase x height

=1/2 BExCF204cm²

=1/2x BEx17BE

=408/17

=24cm

Area of Trapezium =1/2(AB+DF)xBE

=1/2(60+77)x24

=1644cm²