Diagonal to area

Calculate the area of a rectangle in which the length of the diagonal is 10 cm.

Result

S =  36.661 cm2

Solution:

u=10 cm a=4 cm b=u2−a2=102−42=2 21 cm≐9.1652 cm  S=a⋅ b=4⋅ 9.1652=8 21≐36.6606=36.661 cm2u = 10 \ cm \ \\ a = 4 \ cm \ \\ b = \sqrt{ u^2-a^2 } = \sqrt{ 10^2-4^2 } = 2 \ \sqrt{ 21 } \ cm \doteq 9.1652 \ cm \ \\ \ \\ S = a \cdot \ b = 4 \cdot \ 9.1652 = 8 \ \sqrt{ 21 } \doteq 36.6606 = 36.661 \ cm^2

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