A square

A square with 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 length of 16 cm. Calculate the length of the other diagonal.

Result

S =  72 cm2
u3 =  9 cm

Solution:

u1=12 cm  S=a2 u1=2a  S=u122=1222=72 cm2u_{1}=12 \ \text{cm} \ \\ \ \\ S=a^2 \ \\ u_{1}=\sqrt{ 2 }a \ \\ \ \\ S=\dfrac{ u_{1}^2 }{ 2 }=\dfrac{ 12^2 }{ 2 }=72 \ \text{cm}^2
u2=16 cm  S=u2⋅ u32  u3=2⋅ S/u2=2⋅ 72/16=9 cmu_{2}=16 \ \text{cm} \ \\ \ \\ S=\dfrac{ u_{2} \cdot \ u_{3} }{ 2 } \ \\ \ \\ u_{3}=2 \cdot \ S/u_{2}=2 \cdot \ 72/16=9 \ \text{cm}

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