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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 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. _____

 Apr 23, 2021
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(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_

 May 12, 2021

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