Question

If the sides of regular hexagon are increased by 120% then the percentage of change in it's area is​

Answer 1

Answer:

384% ans I hope it is right

Answer 2

Step-by-step explanation:

Solution :-

Let the side of a regular hexagon be a units

We know that

Area of a regular hexagon = (6√3/4)a² sq.units--(1)

If the side of the hexagon Increased by 120% then

The new side

= a+(120% of a)

= a+(120% × a)

= a + (120/100)×a

= a + (6/5)a

= a + (6a/5)

= (5a+6a)/5

= 11a/5

The new side of the new hexagon= 11a/5 units

Then Area of the new hexagon

= (6√3/4)(11a/5)²

= (6√3/4)(121/25)a² sq units------(2)

Increasing in area

= New area - Original area

=(2)-(1)

= [(6√3/4)(121/25)a²]-[(6√3/4)a²]

= (6√3/4)a²[(121/25)-1]

= (6√3/4)a²[(121-25)/25]

=(6√3/4)a²(96/25)

Increasing in area = (96/25)(6√3/4)a² sq.units--(3)

Now

Increased percentage in the area

= (Increasing area/Original area )×100

=[{(96/25)(6√3/4)a²}/{(6√3/4)a²] × 100

= (96/25)×100

=96×100/25

=96×4

= 384%

Answer:-

If the sides of a regular hexagon is Increased by 120% then the Increased percentage in its area is 384%

Used formulae:-

• Area of a regular hexagon = (6√3/4)a² sq.units

Where,a is the side of the regular hexagon.

• A regular hexagon has 6 equilateral triangles

• Area of an equilateral triangle is (√3/4)a² sq units