# Rhombus OWES

OWES is a rhombus given that OW 6cm and one diagonal measures 8cm. Find its area?

Result

S =  35.777 cm2

#### Solution:

$a=6 \ \\ u=8 \ \\ h=\sqrt{ a^2-(u/2)^2 }=\sqrt{ 6^2-(8/2)^2 } \doteq 2 \ \sqrt{ 5 } \doteq 4.4721 \ \\ u_{ 2 }=2 \cdot \ h=2 \cdot \ 4.4721 \doteq 4 \ \sqrt{ 5 } \doteq 8.9443 \ \\ S_{ 1 }=u \cdot \ h/2=8 \cdot \ 4.4721/2 \doteq 8 \ \sqrt{ 5 } \doteq 17.8885 \ \\ S=2 \cdot \ S_{ 1 }=2 \cdot \ 17.8885 \doteq 16 \ \sqrt{ 5 } \doteq 35.7771 \doteq 35.777 \ \text{cm}^2$

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