# The largest angle of a parallelogram measures 120 degrees. If the sides measure 14 inches and 12 inches, what is the exact area of the parallelogram?

*inches*

*We can get the area of parallelogram even though the angle is not given, since you gave the length of the two sides.*

*Area of parallelogram #=bh#*

*#b=14#*

*#h=12#*

*#A=bh#*

*#A=(14)12#*

*#A=168#*

*Sign up to view the whole answer*

*By signing up, you agree to our Terms of Service and Privacy Policy*

*Sign up with email*

*Answer 2Sign up to view the whole answerSign up with email*

To find the exact area of the parallelogram, we can use the formula:

Area = base * height

where the base is any one of the sides of the parallelogram, and the height is the perpendicular distance between the base and its opposite side.

Since the largest angle of the parallelogram measures 120 degrees, the adjacent angles are supplementary, meaning they sum up to 180 degrees. Thus, the other angle measures 60 degrees.

Now, we can use trigonometric ratios to find the height of the parallelogram. The height can be found using the sine of the angle:

sin(60°) = height / 14

Solving for the height, we get:

height = 14 * sin(60°)

Similarly, for the other side, the height is:

height = 12 * sin(120°)

Once we have the heights, we can find the area using the formula mentioned earlier.

By signing up, you agree to our Terms of Service and Privacy Policy

*Answer from HIX Tutor*

*Trending questions*

*Two corners of an isosceles triangle are at #(6 ,4 )# and #(2 ,7 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?**A chord with a length of #9 # runs from #pi/8 # to #pi/6 # radians on a circle. What is the area of the circle?**The diagonal of a rectangle is 3 times as long as the width. If the length is 4 cm, what is the width of the rectangle?**Find the area of a parallelogram with vertices A(1,5,0), B(6,10,−3), C(−4,5,−2), and D(1,10,−5)? Show steps.**A triangle has two corners with angles of # pi / 4 # and # pi / 6 #. If one side of the triangle has a length of #3 #, what is the largest possible area of the triangle?*

*Not the question you need?*

*HIX TutorSolve ANY homework problem with a smart AI*

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7