Question

length of one side of rhombus is 6cm and one angle is 60degree. find the area of the rhombus

Answer 1

Solution:-
given angle is 60degree.
let , length of rhomus AB = 6CM
wide = AC

we have ,
》 tan60 = AC/AB
》
$\sqrt{3} = \frac{ac}{6} \\ ac = 6 \sqrt{3}$
area of rhomus = (6×6√3)/2
》18√3 cm^2

Answer 2

Since, AB=ADAB=AD and ∠BAD=60∘∠BAD=60∘

Therefore, △ABD△ABD is equilateral triangle

Similarly, △CBD△CBD is equilateral triangle

You may be knowing that height of an equilateral triangle is 3–√2⋅side32⋅side

if you want the proof of this, just give a comment

AO=CO=3–√2⋅AB=3–√2⋅10AO=CO=32⋅AB=32⋅10

AC=AO+CO=3–√2⋅10+3–√2⋅10AC=AO+CO=32⋅10+32⋅10

=10√3cm