Answer:
(a)6 Equilateral Triangles.
(b)30-60-90 triangle.
(c)Attached
(d)Length of the short leg = 2cm.
(e)Length of the hypotenuse= 4cm.
(f)Length of the long leg[tex]=2\sqrt{3}[/tex]
(g)Apothem.
(h)Area of One Equilateral triangle [tex]=4\sqrt{3}\:cm^2[/tex]
(i)Area of Hexagon =[tex]=24\sqrt{3}\:cm^2[/tex]
Step-by-step explanation:
(a)There are 6 Equilateral Triangles.
(b)If we cut an equilateral down the middle (green line), we get a 30-60-90 triangle.
(c)Triangle Attached in 3rd diagram.
(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
[tex]4^2=2^2+x^2\\x^2=4^2-2^2=12\\x=\sqrt{12}\\ x=2\sqrt{3}[/tex]
(g)The vocabulary word for the long side of the 30-60-90 called in the polygon (green line) is Apothem.
(h)Area of One Equilateral triangle
Base =4 cm, Height =[tex]2\sqrt{3} cm[/tex]
Area
[tex]=0.5X4X2\sqrt{3}\\=4\sqrt{3}\:cm^2[/tex]
(i)Area of Hexagon =Area of One Equilateral Triangle X 6
=[tex]6X4\sqrt{3}=24\sqrt{3}\:cm^2[/tex]
