Question

The sides of a rhombus with angle of 60° are 6 inches. find the area of the rhombus. 9√3 in2 18√3 in2 36 in2

Answer 1

Drop a perpendicular from an obtuse vertex.

That makes a 30 - 60º right triangle, with

hypotenuse 6 and short leg 3. So the long leg,

which is the height of the rhombus, is 3√3 .

Since a rhombus is a parallelogram, its area

is base x height = 6 x 3√3 = 18√3 .

Answer 2

Drop a perpendicular from an obtuse vertex.

That makes a 30 - 60º right triangle, with hypotenuse 6 and short leg 3. So the long leg, which is the height of the rhombus, is 3√3 .

Since a rhombus is a parallelogram, its area is base x height = 6 x 3√3 = 18√3