Equilateral triangles: height and area

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Learn it An equilateral triangle with side s has height $\frac{\sqrt{3}}{2}s$ (Pythagoras on half the triangle) and area $\frac{\sqrt{3}}{4}s^2 \approx 0.433s^2$.

Example: Find the height and area of an equilateral triangle with side 10 cm.

Height: $\sqrt{10^2 - 5^2} = \sqrt{75} \approx 8.66$ cm.
Area: $\frac{1}{2} \times 10 \times 8.66 \approx 43.3$ cm².
Exact: $\frac{\sqrt{3}}{4} \times 100 = 25\sqrt{3}$ cm².

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