Question

In a trapezium ABCD , AB || CD , AB = 6cm , BC = 5cm , CD - 3 = cm and DA = 4cm . Then area ABCD =

Answer 1

in ∆AOD,
AD²=AO²+OD²
OD²=AD²-AO²
OD²= 4²-(3-x)²
OD²=16-(9+x²-6x)
OD²=16-9-x²+6x
OD²=7-x²+6x
in∆CPB,
CB²=CP²+PB²
CP²=CB²-PB²
CP²=5²-x²
CP²=25-x²
since , OD= CP
THEREFORE, OD²=CP²
7+6x-x²=25-x²
6x=25-7
x=3
that is our trapezium will look like [THE 2ND THUMBNAIL]
area of trapezium
= 1/2(sum of parallel sides)×(height)
=½(3+6)(4)
=2×9
=18cm²