Answer:
The area of a rhombus is [tex]18\sqrt{3}[/tex] square units.
Step-by-step explanation:
Side length of rhombus = 6 units.
Interior angle of rhombus = 120°
another Interior angle of rhombus = 180°-120° = 60°.
Draw an altitude.
In a right angled triangle
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]
[tex]\sin (60)=\frac{h}{6}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{h}{6}[/tex]
Multiply both sides by 6.
[tex]3\sqrt{3}=h[/tex]
The height of the rhombus is [tex]3\sqrt{3}[/tex].
Area of a rhombus is
[tex]Area=base\times height[/tex]
[tex]Area=6\times 3\sqrt{3}[/tex]
[tex]Area=18\sqrt{3}[/tex]
Therefore, the area of a rhombus is [tex]18\sqrt{3}[/tex] square units.
Area of Rhombus is 31.176 unit² (Approx.)
Length of rhombus side = 6 unit
Angle = 120°
Area of Rhombus
Area of Rhombus = Side²(Sin θ)
Area of Rhombus = 6²(Sin 120)
Area of Rhombus = 36(0.866)
Area of Rhombus = 31.176 unit² (Approx.)
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