Question

A parallelogram has sides A, B, C, and D. Sides A and B have a length of `1` and sides C and D have a length of `2`. If the angle between sides A and C is `(3 pi)/4`, what is the area of the parallelogram?

Answer 1

area of given parallelogram is `1.4142`

Explanation:

Area of a parallelogram with sides `a` and `b` and included angle `theta` is given by `axxbxxsintheta`.

Note that in a parallelogram. while one angle is `theta`, other angle is `(180^o-theta)` and as `sin(180^o-theta)=sintheta`, which ever angle we may choose, area is not affected.

As two sides are `1` and `2` and included angle is `(3pi)/4` and

area of given parallelogram is

`1xx2xxsin((3pi)/4)=2xx1/sqrt2=sqrt2=1.4142`