Respuesta :

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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]
qoiop314
*incorect caculations do not read*
we have a formula for that
[tex] {r}^{2} = \frac{5 {a}^{2} }{4} [/tex]
r being the radius and a being the edge of our square

a is
[tex] \sqrt{32} [/tex]
so lets find r
[tex] {r}^{2} = \frac{5 \times { \sqrt{32} }^{2} }{4} [/tex]
after solving we reach these two answers
[tex]r = - 2 \sqrt{10} \\ r = 2 \sqrt{10} [/tex]
we are looking for a radius so negetive numbers are disregarded. now that we have the radius for our semi circle we can calculate the area of our semi circle. with this formula
[tex] \frac{\pi \times {r}^{2} }{2} [/tex]
(just the formula for the area of a circle divided by half)
[tex]area = \frac{\pi \times 2\sqrt{10} }{2} \\area = \pi \times 20 [/tex]

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