Question

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram. 

 

Answer 1

Parallelogram ABCD is made up of congruent `ΔABC and ΔADC`  

Area of triangle ABC= `sqrt (s (s-a)(s-b)(s-c))` 

Thus, we have : 

`s=(a+b+c)/2` 

`s=(34+20+42)/2` 

`s=48 cm` 

Area of Δ ABC=`sqrt(48(48-34)(48-20)(48-42))` 

  =`sqrt(48xx14xx28xx6)` 

=`336 cm^2` 

Now,

Area of the parallelogram=`2xx `Area of ΔABC 

=`2xx336` 

=`672 cm^2`