A square of area 32 cm2 is inscribed into a semi-circle. What is the area of the semi-circle?

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Find Length of the square :
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Given that the area of the square is 32 cm²: 

Area = Length²

[tex]\text {Length =} \sqrt{32} [/tex]

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Find Radius :
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Using Pythagorus Theorem to find the radius of the circle:

a² + b² = c²

[tex]( \sqrt{32})^2 + (\frac{ \sqrt{32} }{2} )^2 = ( \text {radius} )^2[/tex]

[tex](\text {radius} )^2 = 32 + \dfrac{32}{4} [/tex]

[tex](\text {radius} )^2 = 40[/tex]

[tex]\text { Radius = } \sqrt{ 40 } [/tex]

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Find Area of the semi-circle :
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[tex]\text {Area of the semi-circle = } \dfrac{1}{2} \pi r^2[/tex]

[tex]\text {Area of the semi-circle = } \dfrac{1}{2} \pi ( \sqrt{40}) ^2[/tex]

[tex]\text {Area of the semi-circle = } 20 \pi [/tex]

[tex]\text {Area of the semi-circle = } 62.83 \ cm^2[/tex]