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The figure below shows a regular hexagon with sides of length a and a square with sides of length a. If the area of the hexagon is 384√3 square inches, what is the area, in square inches, of the square?
A regular hexagon is a two-dimensional geometrical shape that is made of six equal sides.
Answer: For a regular hexagon with sides of length a and a square with sides of length a, given area of the hexagon as 384√3 square inches, the area of the square is 256 square inches.
Let's look into the steps below
A regular polygon has equal sides and equal angles.
Thus, the measure of all the sides of the regular hexagon given is 'a'.
Area of the hexagon = 384√3 square inches (Given)
We know that,
Area of a Regular Hexagon = (3√3 a2) / 2, where, a = Side length of the Hexagon
⇒ 384√3 = (3√3 a2) /2 [ Since, Area = 384√3 square inches]
⇒ a2 = (384 × 2) / 3
⇒ a2 = 256
Taking square root on both sides,
⇒ a = 16
Now, the side length of the square is given as 'a'
Area of the square = a2
⇒ a2 = 162
⇒ a2 = 256
Thus, the area of the square is 256 square inches.