Question

Please I need help with these, use the picture to answer the questions below

Each dashed line segment is a(n)?


There are _____ congruent triangles in a regular hexagon.


Find the perimeter.


Find the radius of this hexagon.

Answer 1

• 6 congruent traingles

Side Be a

`\\ \rm\rightarrowtail h=(√(3))/(2)a`

`\\ \rm\rightarrowtail 6=(√(3))/(2)a`

`\\ \rm\rightarrowtail 12=√(3)a`

`\\ \rm\rightarrowtail a=12/√(3)`

`\\ \rm\rightarrowtail a=4√(3)`

Perimeter:-

• 4(4√3)=16√3units

Answer 2

There are 6 congruent triangles in a regular hexagon.

The triangles are equilateral (all sides are equal in length).

Using side length of equilateral triangle formula:

`\sf x=\sqrt{(4)/(3)h^2}`

where x is the side length and h is the height

`\sf \implies x=\sqrt{(4)/(3)\cdot 6^2}`

`\sf \implies x=√(48)`

`\sf \implies x=4√(3) \ units`

Therefore, perimeter = 6 × 4√3 = 24√3 units

Radius = side length of triangle = 4√3 units