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?

×
18

✓
9\sqrt{3}

×
12

×
6\sqrt{3}
The figure below is an equilateral triangle. What is the area of the triangle if the length of the sides is 6?
18
9\sqrt{3}
12
6\sqrt{3}
Since \triangle ABC is an equilateral triangle, the height h and the sides of the triangle makes a 306090 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}