What is the ratio of the interior angle of a regular hexagon to the interior angle of a regular 12-sided polygon (dodecagon)?
4:5
The interior angle of a regular polygon with \(n\) sides is \(\frac{(n-2)\times 180^\circ}{n}\).
For the hexagon, \(n=6\): interior angle \(= \frac{(6-2)\times 180^\circ}{6} = \frac{4\times 180^\circ}{6} = 120^\circ\).
For the dodecagon, \(n=12\): interior angle \(= \frac{(12-2)\times 180^\circ}{12} = \frac{10\times 180^\circ}{12} = 150^\circ\).
Required ratio \(= 120^\circ : 150^\circ = \frac{120}{150} = \frac{4}{5} = 4:5\).
Hence, the ratio is 4:5.
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If ∆ABC ~ ∆DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm 2, then the area of the triangle DEF is:
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If ΔABC and ΔDEF are congruent triangles, then which of the following is FALSE?
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