Silver medal

To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?

Correct result:

S =  50 cm2

Solution:

D=10 cm D2=a2+(3a)2 D2=a2+9a2 D2=10 a2  D=10a a=D/10=10/1010 cm3.1623 cm n=5  S=n a2=5 3.16232=50 cm2D=10 \ \text{cm} \ \\ D^2=a^2 + (3a)^2 \ \\ D^2=a^2 + 9a^2 \ \\ D^2=10 \ a^2 \ \\ \ \\ D=\sqrt{ 10 } a \ \\ a=D / \sqrt{ 10 }=10 / \sqrt{ 10 } \doteq \sqrt{ 10 } \ \text{cm} \doteq 3.1623 \ \text{cm} \ \\ n=5 \ \\ \ \\ S=n \cdot \ a^2=5 \cdot \ 3.1623^2=50 \ \text{cm}^2



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