Problems from The rhombus

Development:

1. A square is defined with its side $l=6$ cm.

2. Note that the axes of the inscribed rhombus ($D$ and $d$) measure the same as the side of the square $l$. $$D=6\text{cm}$$ $$d=6\text{cm}$$

3. The area of the square is: $$A=(6\text{cm}{)}^2=36{\text{cm}}^2$$

4. The area of the rhombus is: $$A_{rhombus}={\displaystyle \frac{D\cdot d}{2}}=18{\text{cm}}^2={\displaystyle \frac{A_{square}}{2}}$$

See that the inscribed rhombus is also a square of side $\sqrt{18}=3\sqrt{2}.$

Thus, the side of the rhombus could also have been calculated (with the Pythagorean theorem) and then squared to obtain the area.

Solution:

1. $l=6$ cm
2. $D=6$ cm, $d=6$ cm
3. $A=36{\text{cm}}^2$
4. $A_{rhombus}=18{\text{cm}}^2$

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