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7 December, 02:58

What is the area of an equilateral triangle with radius 15 centimeters? Round your answers to the nearest tenth, if necessary.

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  1. 7 December, 03:27
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    Radius is 2/3 of the height of an equilateral triangle.

    15 = 2/3 h

    h = 15 : 2/3 = 15 · 3/2 = 45/2 = 22.5 cm

    a · cos 30° = h

    a · √3/2 = h

    a = 45/√3 = 15√3 cm

    A = 1/2 · a · h = 1/2 · 15√3 · 22.5 = 0.5 · 15 · 1.7320508 · 22.5

    A = 292.28 ≈ 292.3 cm²
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