What is the surface area of an equilateral triangle featuring side lengths of 16 cm?
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Answer: D. 64√3 cm2
Explanation
The formula for the area of an equilateral triangle requires multiplying root three over four by the side squared. Squaring sixteen gives two hundred fifty six square centimeters for the intermediate calculation. Multiplying two hundred fifty six by root three over four yields sixty four root three square centimeters. An equilateral triangle features three sides of equal length and three internal angles of sixty degrees. The height of an equilateral triangle is calculated as root three over two times the side length. Area formulas for triangles derive from one half multiplied by the base and the perpendicular height.
Structural engineering utilizes triangular trusses because equilateral configurations distribute loads efficiently. Tessellation patterns in design often incorporate equilateral triangles for aesthetic and structural stability. Geodesic domes are constructed using interconnected triangular panels based on these precise geometric properties. Option A results from incorrectly dividing the squared side coefficient during simplification. Option B miscalculates the fraction multiplier by using an incorrect denominator in the formula. Option C underestimates the surface area due to an improper decimal placement in the calculation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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