The sides of a rhombus with an angle of 60° are 6 inches. Find the area of the rhombus.

Solution:

It is given that the sides of a rhombus with an angle of 60° are 6 inches.

Drop a perpendicular from an obtuse vertex.

That makes a 30 - 60º right triangle,

With hypotenuse 6 and short leg 3.

Then the long leg, which is the height of the rhombus, is 3√3.

Since a rhombus is a parallelogram,

So, area of rhombus = base x height

= 6 x 3√3

= 18√3

Therefore, the area of the rhombus is 18√3 square inches.

The sides of a rhombus with an angle of 60° are 6 inches. Find the area of the rhombus.

Summary:

The sides of a rhombus with an angle of 60° are 6 inches. The area of the rhombus is 18√3 square inches.