A rhombus has each side of length $5\text{cm}$ and one interior angle of $60^{\circ }$. Find its area in ${\text{cm}}^2$.

Step-by-step solution

1. Step 1: Area of a rhombus can be expressed as $A=a^{2}sin\theta$, where $a$ is the side length and $\theta$ is any interior angle.
2. Step 2: Take $a=5\text{ cm}$ and $\theta =60^{\circ }$.
3. Step 3: Recall $\sin 60^{c}irc=\frac{\sqrt{3}}{2}$.
4. Step 4: Substitute the values: $A=5^2\times \frac{\sqrt{3}}{2}=25\times \frac{\sqrt{3}}{2}$.
5. Step 5: Simplify to get $A=\frac{25\sqrt{3}}{2}{\text{cm}}^2\approx 21.65{\text{cm}}^2$.

Concept tested: Area of rhombus using interior angle

Published 16 October 2026 · How this solution was prepared and checked