Question

if the area of a regular hexagon is 24√3 cm^2 the find its perimeter​

Answer 1

Answer:

24cm

Step-by-step explanation:

area of a regular hexagon 3√3/2a^2=24√3

a^2=16

a=4

perimeter=6a=6×4=24cm

Answer 2

GIVEN:-

• $\tt{Area\:of\:regular\:hexagon = 24\sqrt{3}cm^2}$

TO FIND:-

• The Perimeter of the hexagon.

FORMULAE USED:-

• ${\boxed{\rm{Area\:of\:hexagon= 3\dfrac{\sqrt{3}a^2}{2}}}}$.

Now,

$\implies\rm{Area\:of\: hexagon = 3\dfrac{\sqrt{3}a^2}{2}}$

$\implies\rm{ 24\sqrt{3}cm^2 = 3\dfrac{\sqrt{3}a^2}{2}}$

$\implies\rm{ 24\times{2} = 3 \times{a^2}}$

$\implies\rm{ \dfrac{48}{3} = a^2}$

$\implies\rm{ 16 = a^2 }$

$\implies\rm{ a = 4cm}$

As we know that hexagon has 6 sides.

Perimeter of Hexagon = 6a = 24cm.

Hence, The Perimeter of Hexagon is 24cm.