# 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:

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

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