# 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:

$u_{1}=8 \ \text{cm} \ \\ u_{2}=12 \ \text{cm} \ \\ a^2=(u_{1}/2)^2 + (u_{2}/2)^2 \ \\ a=\sqrt{ (u_{1}/2)^2 + (u_{2}/2)^2 }=\sqrt{ (8/2)^2 + (12/2)^2 } \doteq 2 \ \sqrt{ 13 } \doteq 7.2111 \doteq 7.211 \ \text{cm}$
$S=u_{1} \cdot \ u_{2}/2=8 \cdot \ 12/2=48 \ \text{cm}^2$

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