Question

Construct a rhombus FARM with FR = 7 cm and
∠ F= 80° . Also find its area.

Answer 1

Given: $FR=7cm$ and $\angle F={80}^{\circ }$


Steps:
1. Draw a line segment $FR=7cm$.
2. At F, make $\angle RFX=\angle RFY={40}^{\circ }$ on either side of $FR$.
3. At $R$, make $\angle FRP=\angle FRQ={40}^{\circ }$ on either side of $F$.
4. Let $FX$ and RP cut at $M$ and $FY$ and RQ cut at $A$.
5. FARM is the required rhombus.
Calculation of Area:
$$\begin{array}{cc}\text{Area of rhombus FARM}& =\frac{1}{2}\times d_1\times d_2\text{sq.units}\\ & =\frac{1}{2}\times 7\times 5.9=20.65sq.cm\end{array}$$
Hence, Area of a rhombus is 20.65 sq.cm