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The side of a square is 20 cmfind the areas of the circumscribed and inscribed circles?
Wiki User
∙ 14y ago
The radius length r of the inscribed circle equals to one half of the length side of the square, 10 cm.
The area A of the inscribed circle: A = pir2 = 102pi ≈ 314 cm2
The radius length r of the circumscribed circle equals to one half of the length diagonal of the square.
Since the diagonals of the square are congruent and perpendicular to each other, and bisect the angles of the square, we have
sin 45⁰ = length of one half of the diagonal/length of the square side
sin 45⁰ = r/20 cm
r = (20 cm)(sin 45⁰)
The area A of the circumscribed circle: A = pir2 = [(20 cm)(sin 45⁰)]2pi ≈ 628 cm2.
Wiki User
∙ 14y ago
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