Question

Two sides of a parallelogram are 24 feet and 30 feet. The measure of the angle between these sides is 57 degrees. What is the area of the parallelogram to the nearest square foot?

Answer 1

`604 ft.^2`

Explanation:

Refer to the figure below

In the given parallelogram, if we draw a line perpendicular to one side measuring 30, from the vertex common with one of the sides measuring 24, the segment formed (when it meets the line in which the other side measuring 30 lays) is the height (`h`).

From the figure we can see that
`sin 57^@=h/24` => `h=24*sin 57^@=20.128 ft.`

The area of a parallelogram is
`S=base*height`

So
`S=30*20.128~=603.84 ft.^2` (rounding the result, `-> 604ft.^2`)