Let PQRSTU be a regular hexagon. The ratio of the area of the triangle PRT to that of the hexagon PQRSTU is
Explanation:
A regular hexagon comprises six equilateral triangles. ∴ Area of hexagon = 6 × area of equilateral triangle = area of six equilateral triangles
P, R and T are alternate vertices of the hexagon. The triangle formed by joining them splits each equilateral triangle into half. Six half-equilateral triangles is equivalent to three equivalent triangles.
∴ Area of triangle PRT = area of three equilateral triangles.
∴ Required ratio = (area of three equilateral triangles) / (area of six equilateral triangles) = 0.5
Hence, option (b).
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