Diamond area from diagonals

In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond?

Correct result:

S =  15.36 dm2

Solution:

a=4 dm u=6.4 dm  a2=(u/2)2+(v/2)2  v=2 a2(u/2)2=2 42(6.4/2)2=245=4.8 dm  S=u v2=6.4 4.82=38425=15.36 dm2a=4 \ \text{dm} \ \\ u=6.4 \ \text{dm} \ \\ \ \\ a^2=(u/2)^2 + (v/2)^2 \ \\ \ \\ v=2 \cdot \ \sqrt{ a^2-(u/2)^2 }=2 \cdot \ \sqrt{ 4^2-(6.4/2)^2 }=\dfrac{ 24 }{ 5 }=4.8 \ \text{dm} \ \\ \ \\ S=\dfrac{ u \cdot \ v }{ 2 }=\dfrac{ 6.4 \cdot \ 4.8 }{ 2 }=\dfrac{ 384 }{ 25 }=15.36 \ \text{dm}^2



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