Question

A parallelogram has sides A, B, C, and D. Sides A and B have a length of `3` and sides C and D have a length of `9`. If the angle between sides A and C is `(7 pi)/18`, what is the area of the parallelogram?

Answer 1

Area of parallelogram is `27xx0.9397=25.372`

Explanation:

If the two pairs of equal sides of a parallelogram gram are `a` and `b` and included angle (whether acute or obtuse) is `theta`, area of a triangle is given by

`axxbxxsintheta`

Hence area of parallelogram whose pair of parallel sides are `3` and `9` and included angle is `((7pi)/18)` is given by `3xx9xxsin((7pi)/18)`

Now angle `(7pi)/18hArr(7pi)/18xx180^o/pi=70^o` and looking at tables `sin70^o=0.9397`

Hence area of parallelogram is `27xx0.9397=25.372`