Multiple Choice Question (MCQ)

The figure below is an equilateral triangle. What is the area of the triangle if the length of the sides is 6?

  1. ×

    18

  2. 9\sqrt{3}

  3. ×

    12

  4. ×

    6\sqrt{3}

Collected in the board: Triangle

Steven Zheng posted 1 month ago

Answer

  1. Since \triangle ABC is an equilateral triangle, the height h and the sides of the triangle makes a 30-60-90 special right angle triangle \triangle BCD . The ratio of the triangle is 1:\sqrt{3} :2.

    Therefore,

    DB = \dfrac{1}{2}BS = 3

    h = CD = \sqrt{3} BD = 3\sqrt{3}

    According to the area formula of a triangle,

    S_{\triangle ABC } = \dfrac{1}{2}AB \cdot h = \dfrac{1}{2}\cdot 6\cdot 3\sqrt{3} = 9\sqrt{3}




Steven Zheng posted 1 month ago

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