Question

A parallelogram has sides A, B, C, and D. Sides A and B have a length of `5` and sides C and D have a length of `8`. If the angle between sides A and C is `pi/3`, what is the area of the parallelogram?

Answer 1

`34.641`

Explanation:

Area of parallelogram is given by `l_1xxl_2xxsintheta`.

In the instant case it will be `5xx8xxsin(pi/3)`

=`40xxsqrt3/2=34.641`

Answer 2

approximately `34.64` sq.units

Explanation:

From the diagram below, we see that
`color(white)("XXX")`the height of the parallelogram (using `A` as the base) is
`color(white)("XXX")8xxsin(pi/3) = 8xxsqrt(3)/2 = 4sqrt(3)`

The area of the parallelogram is
`color(white)("XXX")Axxh = 5xx4sqrt(3) =20 sqrt(3)~~34.64`