Hi All,

We're told that the hexagonal face of the block shown in the figure above has sides of equal length and angles of equal measure and each lateral face is rectangular. We're asked for the area, in square inches, of one lateral face. This question is based on a Geometry pattern - and if you know the pattern then you can answer this question with just a little arithmetic.

We're given a hexagon with equal sides and equal angles. A hexagon has 720 total degrees, meaning that each of the 6 angles is 120 degrees. Thus, we can 'cut up' the hexagon into 6 identical equilateral triangles with side lengths of 12. That makes the area of each rectangle 'face' 12 x 2 = 24 square inches.

Final Answer: E

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Rich

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The hexagonal face of the block shown in the figure above has sides of equal length and angles of equal measure. If each lateral face is rectangular, what is the area, in square inches, of one lateral face?
$$A.\, 2\sqrt{10}$$
$$B.\, 12$$
$$C.\, 20$$
$$D.\, 12\sqrt{3}$$
$$E.\, 24$$

The hexagon has (n - 2) x 180 = 4 x 180 = 720 degrees; thus, each of the 6 angle measures of the hexagon is 120 degrees. We can thus create 6 identical equilateral triangles within the hexagon, with each side of each triangle measuring 12 inches.

Thus, one lateral face is 12 x 2 = 24 square inches.

Answer: E