If the height of an equilateral triangle is 12 cm, then what is the area of the triangle?
Answer & explanation
Correct answer: option 4
Height of the equilateral triangle = 12 cm
Height of triangle = \(\frac{\sqrt {3}}{2}\)× side of an equilateral triangle
Area of an equilateral triangle = \(\frac{\sqrt {3}}{4}\)× side2
Side of the triangle = \(\frac{2}{\sqrt {3}}\)× 12 = 8$\sqrt {3}$
Area of the triangle = \(\frac{\sqrt {3}}{4}\)× (8$\sqrt {3}$)2
= \(\frac{\sqrt {3}}{4}\) × 64 × 3 = $\sqrt {3}$ × 16 × 3 = 48$\sqrt {3}$ = 83.1384 cm2