Diagonals

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

Correct answer:

a =  7.2111 cm
S =  48 cm²

Step-by-step explanation:

$$\begin{gathered} u_1=8\text{ cm } \\ {u}_2=12\text{ cm } \\ {a}^2=(u_1\mathrm{/}2{)}^2+(u_2\mathrm{/}2{)}^2 \\ a=\sqrt{(u_1\mathrm{/}2{)}^2+(u_2\mathrm{/}2{)}^2}=\sqrt{(8\mathrm{/}2{)}^2+(12\mathrm{/}2{)}^2}=2\sqrt{13}=7.2111\text{ cm} \end{gathered}$$

$S=u_1\cdot u_2\mathrm{/}2=8\cdot 12\mathrm{/}2=48{\text{cm}}^2$

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