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 answer:

S =  72 cm²
u₃ =  9 cm

Step-by-step explanation:

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

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

Try another example