A square

A square with a length of diagonals 12cm give:
a) Calculate the area of a square
b) rhombus with the same area as the square, has one diagonal with a length of 16 cm. Calculate the length of the other diagonal.

Correct result:

S =  72 cm²
u₃ =  9 cm

Solution:

$$\begin{gathered} u_1=12\text{ cm } \\ S=a^2 \\ {u}_1=\sqrt{2}a \\ S={\displaystyle \frac{u_1^2}{2}}={\displaystyle \frac{12^2}{2}}=72{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} u_2=16\text{ cm } \\ S={\displaystyle \frac{u_2\cdot u_3}{2}} \\ {u}_3=2\cdot S\mathrm{/}{u}_2=2\cdot 72\mathrm{/}16=9\text{ cm} \end{gathered}$$

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