Question

Find the area of each figure:

A rhombus with a${120}^{\circ }$angle and sides 6cm

Short answer

The area of given figure is$18\sqrt{3}c{m}^3$

Step-by-step solution

Step 1. Given information.

Rhombus with angle${120}^{\circ }$ and sides of the rhombus are$$" width="9" height="19" role="math">

Step 2. Concept used.

Area of rhombus can be found using the formula

$A={\left(side\right)}^2\times sin\theta$

Step 3. Find the area of given figure.

$A={\left(side\right)}^2\times sin\theta$

$={\left(6\right)}^2\times sin{120}^{\circ }$

$=36\times \frac{\sqrt{3}}{2}$

$=18\sqrt{3}c{m}^3$

Therefore, the area of given figure is$18\sqrt{3}c{m}^3$ .