Question

Score for Question 3: ___ of 5 points)

Answer 1

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=$2\sqrt{3}cm$

(g)Apothem.

(h)Height of the Equilateral triangle=$2\sqrt{3}cm$

(i)Area of One Equilateral triangle =$4\sqrt{3}cm^2$

(j)Area of Hexagon =$=24\sqrt{3}\:cm^2$

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.

$4^2=2^2+l^2\\l^2=4^2-2^2=12\\l=\sqrt{12}=2\sqrt{3}cm$

(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=$2\sqrt{3}cm$

(i)Area of One Equilateral triangle

Base =4 cm, Height =$2\sqrt{3}cm$

Area=0.5X4X$2\sqrt{3}cm$

=$4\sqrt{3}\:cm^2$

(j)Area of Hexagon =Area of One Equilateral Triangle X 6

$=6X 4\sqrt{3}\\=24\sqrt{3}\:cm^2$