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?

Question

Sadie Allen · Accepted Answer

#604 ft.^2#

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#)

Autumn Armstrong · Answer

undefined To find the area of the parallelogram, you can use the formula: Area = base × height. In a parallelogram, the base is one of its sides, and the height is the perpendicular distance between this base and the opposite side.

Since the angle between the given sides is 57 degrees, you can use trigonometric functions to find the height. The height can be calculated as follows: height = side * sin(angle).

Given that one side is 24 feet and the angle between the sides is 57 degrees, you can calculate the height:

height = 24 * sin(57°)

Now, find the area using the calculated height and the other side length:

Area = base * height
     = 30 * height

Once you have the value of the height, plug it into the formula and calculate the area. Finally, round the result to the nearest square foot.