If the height of an equilateral triangle is 12 cm, then what is the area of the triangle?
Answer
The correct answer is B: 83.1384 cm². For an equilateral triangle with height h, side a = 2h/√3 = 24/√3. Area = (√3/4)a² = (√3/4)(576/3) = 48√3 ≈ 83.14 cm².
A.89.567 cm²
B.83.1384 cm²✓ Correct
C.96.897 cm²
D.67.9843 cm²
Explanation
For an equilateral triangle with height h, side a = 2h/√3 = 24/√3. Area = (√3/4)a² = (√3/4)(576/3) = 48√3 ≈ 83.14 cm².
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