# Rhombus

Calculate the perimeter and area of ​​a rhombus whose diagonals are 39 cm and 51 cm long.

Result

p =  128.406 cm
S =  994.5 cm2

#### Solution:

$u_{1}=39 \ \text{cm} \ \\ u_{2}=51 \ \text{cm} \ \\ \ \\ a^2=(u_{1}/2)^2+(u_{2}/2)^2 \ \\ a=\sqrt{ (u_{1}/2)^2+(u_{2}/2)^2 }=\sqrt{ (39/2)^2+(51/2)^2 } \doteq 32.1014 \ \text{cm} \ \\ \ \\ p=4 \cdot \ a=4 \cdot \ 32.1014 \doteq 6 \ \sqrt{ 458 } \doteq 128.4056 \doteq 128.406 \ \text{cm}$
$S=\dfrac{ u_{1} \cdot \ u_{2} }{ 2 }=\dfrac{ 39 \cdot \ 51 }{ 2 }=\dfrac{ 1989 }{ 2 }=994.5 \ \text{cm}^2$

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