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 8 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 (red line), what special right triangle do you create? _____
(4) What is the vocabulary word for the green line? _____
(5) What is the length of the short side of one 30-60-90 triangle? _____
(6) What is the length of the hypotenuse of one 30-60-90 triangle? _____
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg. _____
(8) What is the height of the equilateral triangle? _____
(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. _____
(1) How many equilateral triangles are there? ___6__
(2) What is the measure of each of the three angles in the equilateral triangle? __60°_
(3) If we cut an equilateral triangle down the middle (green line), what special right triangle do you create? _30-60-90_
(4) What is the vocabulary word for the green line? _Perpendicular bisector_
(5) What is the length of the short side of one 30-60-90 triangle? __4_cm_
(6) What is the length of the hypotenuse of one 30-60-90 triangle? __8 cm
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg. _4√3_cm
(8) What is the height of the equilateral triangle? _4√3_cm
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. ½(8)(4√3) = 16√3 cm²
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _8(16√3) = 128√3 cm²_
