A rhombus has an angle measure of 120, and its longer diagonal has a length of 10 inches. Find the area of the rhombus.
Solution
To find the area of the rhombus
In a rhombus opposite angles are equal and it contains
2 triangle (sum of degree is 2*180)
so angles are 120, 60, 120, 60.
and all four sides are of equal length.( = 6)
Area of rhombus is
where a is the length of a diagonal
and b is the length of the other diagonal
if we connect 120 degrees angles to each other will have 2
Equilateral
it means the shorter diagonal is 6.
and if we connect 60 degrees opposite angles to each other we will
have two Rectangular.
a² = b² + c²
we can find longer diagonal
36 = b² + 9
b = 5.196
then longer diagonal is 10.39
Area is
but we have other formula
where s is the length of
any side
and A is any interior
angle
by this formula
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