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Home » Calculate \( (1.5)^4 \): - Groen Casting

Calculate \( (1.5)^4 \): - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A = \sqrt{15 \cdot 8 \cdot 10} = \sqrt{1200} = \sqrt{400 \cdot 3} = 20\sqrt{3}

📌 r = \frac{A}{s} = \frac{20\sqrt{3}}{15} = \frac{4\sqrt{3}}{3}

📌 Thus, the radius of the inscribed circle is $ \boxed{\dfrac{4\sqrt{3}}{3}} $ cm.

📌 Question: An entomologist observes a spiderweb forming a perfect equilateral triangle with side length 12 cm. What is the area of the circle that circumscribes this triangle?

📌 For an equilateral triangle of side length $ s = 12 $, the circumradius $ R $ is given by the formula:

📌 R = \frac{s}{\sqrt{3}}

📌 But more accurately, the correct formula for the circumradius of an equilateral triangle is:

📌 R = \frac{s}{\sqrt{3}} \cdot \frac{2}{3} \cdot \text{height} = \frac{s}{\sqrt{3}} \cdot \frac{2}{3} \cdot \frac{\sqrt{3}}{2}s = \frac{s}{\sqrt{3}} \cdot \frac{\sqrt{3}}{2} \cdot \frac{2}{3} \cdot s

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