Diagonals

Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.

Result

a =  7.211 cm
S =  48 cm2

Solution:

u1=8 cm u2=12 cm a2=(u1/2)2+(u2/2)2 a=(u1/2)2+(u2/2)2=(8/2)2+(12/2)2≐2 13≐7.2111≐7.211 cmu_{1}=8 \ \text{cm} \ \\ u_{2}=12 \ \text{cm} \ \\ a^2=(u_{1}/2)^2 + (u_{2}/2)^2 \ \\ a=\sqrt{ (u_{1}/2)^2 + (u_{2}/2)^2 }=\sqrt{ (8/2)^2 + (12/2)^2 } \doteq 2 \ \sqrt{ 13 } \doteq 7.2111 \doteq 7.211 \ \text{cm}
S=u1⋅ u2/2=8⋅ 12/2=48 cm2S=u_{1} \cdot \ u_{2}/2=8 \cdot \ 12/2=48 \ \text{cm}^2

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