Question
Download Solution PDFAn equilateral triangle with side a units is cut on the vertices to make it a regular hexagon. What is the area of the hexagon?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Side of equilateral triangle = a units
Concept:
Area of an equilateral triangle = √3/4 × side²
For the hexagon to have equal sides the length of the sides of the hexagon should be one third the length of the sides of the equilateral triangle.
Calculation:
Side of hexagon = Side of equilateral triangle/3 = a/3 units
⇒ Area of hexagon = 6 × Area of equilateral triangle = 6 × √3/4 × (a/3)² = a²/2√3 square units
Hence, the area of the hexagon is \(\rm\frac{a^2}{2\sqrt{3}}\) square units.
Last updated on Jun 30, 2025
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