One angle of a rhombus is 120 degrees. The perimeter
is 96m. Find the Area.
A rhombus is a parallelogram with all four sides equal:
_____________
/ /
/ /
/ /
/ /
/ /
¯¯¯¯¯¯¯¯¯¯¯¯¯
The formula for the area of any parallogram is bh
So we draw in the height, h. The perimeter is 96,
and since a rhombus has four equal sides, each side
is 1/4 of 96m, or 24m. Also since the measure
of the obtuse interior angle on the lower right
corner is 120°, the acute angle on the lower left
corner must be supplementary to it, or 180°-120°
which is 60°:
_____________
/| 24m /
/ | /
24m/ |h / 24m
/ | /
/60° | 120°/
¯¯¯¯¯¯¯¯¯¯¯¯¯
Now from the right triangle on the left of the
rhombus,
h
sin(60°) = ----
24
Multiply both sides by 24:
24·sin(60°) = h
_
24(Ö3/2) = h
Simplify:
_
12Ö3 = h
The formula for the area is
A = base×height
The base is the bottom side which is 24m
_
The height is h which is 12Ö3
_
So A = (24)(12Ö3)
_
A = 288Ö3 or approximately 498.83063276
I'd round that off to 499m², or however your
teacher tells you.
Edwin
