# Diagonals of diamond

Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.

Result

S =  82.5 m2
o =  37.202 m

#### Solution:

$u_{ 1 } = 15 \ m \ \\ u_{ 2 } = 11 \ m \ \\ S = \dfrac{ u_{ 1 } \cdot \ u_{ 2 } }{ 2 } = \dfrac{ 15 \cdot \ 11 }{ 2 } = \dfrac{ 165 }{ 2 } = 82.5 = 82.5 \ m^2$
$a = \sqrt{ (u_{ 1 }/2)^2+(u_{ 2 }/2)^2 } = \sqrt{ (15/2)^2+(11/2)^2 } \doteq 9.3005 \ m \ \\ o = 4 \cdot \ a = 4 \cdot \ 9.3005 = 2 \ \sqrt{ 346 } \doteq 37.2022 = 37.202 \ \text{ m }$

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