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Home » \cos 45^\circ = \frac{\sqrt2}2 - Parker Core Knowledge

\cos 45^\circ = \frac{\sqrt2}2 - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Thus, the area decreases by \(\boxed{8}\) square centimeters.

📌 Question:** A circle is inscribed in a square with side length 10 cm. What is the area of the shaded region outside the circle but inside the square, expressed in terms of \(\pi\)?

📌 The side length of the square is 10 cm, so its area is:

📌 A_{\text{square}} = 10^2 = 100 \text{ cm}^2

📌 The circle is inscribed, so its diameter equals the side of the square, 10 cm, meaning the radius \(r\) is:

📌 r = \frac{10}{2} = 5 \text{ cm}

📌 The area of the circle is:

📌 A_{\text{circle}} = \pi r^2 = \pi \cdot 5^2 = 25\pi \text{ cm}^2

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