Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. If T is the mid point of CD, then the length of AT, in cm, is
Explanation:
Side of the regular hexagon = 2 cm. Consider the figure below.
Consider the isosceles ∆ATF
TU is the altitude from T to AF. We know, in a regular hexagon the distance between any two parallel sides = √3 × side. ∴ TU = √3 × 2 = 2√3 cm.
Since ATF is an isosceles triangle, U will be the mid-point of AF ∴ AU = 1 cm.
In ∆ATU AT2 = TU2 + AU2 ⇒ AT2 = (2√3)2 + 12 ⇒ AT2 = 13 ⇒ AT = √13
Hence, option (c).
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