Q14. - Geometry

Question

Find the area of each figure:

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

Step-by-Step Solution

Answer

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

Step 1. Given information.

Rhombus with angle${120}^{\circ }$ and sides of the rhombus are $$" width="9" height="19" style="max-width: none; vertical-align: -4px;" >

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