If the height of an equilateral triangle is 12 cm, then what is the area of the triangle?

83.1384 cm²

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