Answer:
(a)6 Equilateral Triangles.
(b)30-60-90 triangle.
(c)See Attached Triangle in Figure 2
(d)Length of the short leg = 2cm.
(e)Length of the hypotenuse= 4cm.
(f)Length of the long leg=[tex]2\sqrt{3}cm[/tex]
(g)Apothem.
(h)Height of the Equilateral triangle=[tex]2\sqrt{3}cm[/tex]
(i)Area of One Equilateral triangle =[tex]4\sqrt{3}cm^2[/tex]
(j)Area of Hexagon =[tex]=24\sqrt{3}\:cm^2[/tex]
Step-by-step explanation:
(a)From Figure 1, there are 6 Equilateral Triangles.
(b)If we cut an equilateral down the middle (green line), we create a 30-60-90 triangle.
(c)Triangle Attached in Figure 2.
(d)The length of the short leg of one of the 30-60-90 triangle is 2cm.
(e)The length of the hypotenuse of one of the 30-60-90 triangle is 4cm.
(f)Length of the long leg
We use Pythagoras Theorem to find the length of the long leg of the right triangle.
[tex]4^2=2^2+l^2\\l^2=4^2-2^2=12\\l=\sqrt{12}=2\sqrt{3}cm[/tex]
(g)The vocabulary word for the long side of the 30-60-90 called in the polygon (green line) is Apothem.
It is line segment from the center to the midpoint of one of the sides of a polygon.
(h)Height of the Equilateral Triangle=[tex]2\sqrt{3}cm[/tex]
(i)Area of One Equilateral triangle
Base =4 cm, Height =[tex]2\sqrt{3}cm[/tex]
Area=0.5X4X[tex]2\sqrt{3}cm[/tex]
=[tex]4\sqrt{3}\:cm^2[/tex]
(j)Area of Hexagon =Area of One Equilateral Triangle X 6
[tex]=6X 4\sqrt{3}\\=24\sqrt{3}\:cm^2[/tex]
