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

Answer:

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:

$\sf x=\sqrt{\dfrac{4}{3}h^2}$

where x is the side length and h is the height

$\sf \implies x=\sqrt{\dfrac{4}{3}\cdot 6^2}$

$\sf \implies x=\sqrt{48}$

$\sf \implies x=4\sqrt{3} \ units$

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

Radius = side length of triangle = 4√3 units

Answer 2

• 6 congruent traingles

Side Be a

$\\ \rm\rightarrowtail h=\dfrac{\sqrt{3}}{2}a$

$\\ \rm\rightarrowtail 6=\dfrac{\sqrt{3}}{2}a$

$\\ \rm\rightarrowtail 12=\sqrt{3}a$

$\\ \rm\rightarrowtail a=12/\sqrt{3}$

$\\ \rm\rightarrowtail a=4\sqrt{3}$

Perimeter:-

• 4(4√3)=16√3units