Question

A parallelogram has sides A, B, C, and D. Sides A and B have a length of `7` 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

`7sqrt2` squnit

Explanation:

The diagonal of the parallelogram bisects it.
So in this case area of the parallelogram is
= 2X area of the triangle formed by sides A and C
= 2X`1/2ACSintheta`, whwre `theta= angle between A ,C =3pi/4`
So area `=2.(1/2).7.2.sin(3pi/4)=14*sin(pi/4)=14*1/sqrt2=7sqrt2`squnit