Question 986276
.
The area of the parallelogram is twice the area of the triangle with the side measures of  34 cm,  20 cm  and  42 cm. 


Use the Heron's formula for the area of a triangle &nbsp;(see the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Surface-area/-Proof-of-the-Heron%27s-formula-for-the-area-of-a-triangle.lesson>Proof of the Heron's formula for the area of a triangle</A>&nbsp; in this site). 


The semi-perimeter of the triangle is &nbsp;{{{s}}} = {{{(34+20+42)/2}}} = {{{96/2}}} = 48 cm. 


Then the area of the triangle is &nbsp;{{{A}}} = {{{sqrt(48*(48-42)*(48-20)*(48-34))}}} = 336 {{{cm^2}}}.


Hence, &nbsp;the area of the parallelogram is twice this value, &nbsp;i.e. 672 {{{cm^2}}}.