A rhombus having each side 10 cm has one of its angles as 120∘, then the area of the rhombus will be equal to
50√3 cm2
Let ABCD be the rhombus in which AB=AD=10 cm ∠B=120∘ as shown in figure
∠A=180∘−120∘=60∘
Draw DE perpendicular to AB
In Δ AED, ∠ A=60∘, ∠ AED=90∘, ∠ ADE=30∘
The corresponding sides can be calculated as
⇒sin(30):sin(60):sin(90)
⇒12:√32:1
⇒1:√3:2
In a 30-60-90 right angled triangle, the sides are in the ratio 1 : √3 : 2
i.e AE : DE : AD = 1 : √3 : 2
Hence, let the sides be x , √3x , 2x
Given, 2x = 10 cm, ⇒ x = 5 cm
Therefore DE = 5√3 cm
Area of rhombus = AB×DE
=10×5√3=50√3 cm2