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Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 12 cm.
(1) How many equilateral triangles are there? _____
(2) What is the measure of each of the three angles in the equilateral triangle? _____
(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____
(4) What is the vocabulary word for the segment a? _____
(5) What is the length of the short side of one of the 30-60-90 triangles? _____
(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____
(8) What is the height of one of the the equilateral triangles? _____
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____
