Question

A wire was bent to form a square of side 21cm. The same wire was then straightened and rebent to form a regular square hexagon. Find the length of each side of the hexagon.​

Answer 1

Answer:

Given:-

Number of sides in hexagon : 6

Perimeter of regular hexagon : 21

To find:-

the value of one side

Solution:-

X+X+X+X+X+X = 21

=> 6X  =  21

X  =  21/6

X  =  7/2

X  = 3.5 CM

Step-by-step explanation:

Answer 2

$\bigstar$ EXPLANATION $\bigstar$

• Question

A wire was bent to form a square of side 21cm. The same wire was then straightened and rebent to form a regular square hexagon. Find the length of each side of the hexagon?

• Procedure

As the same wire is first bent into a square and then again into a hexagon

That means the length of wire didn't change

Therefore,

The perimeter of the two figures made are equal

Side of the square made using the wire = 21 cm

We know that,

The Perimeter of the square = $4 * (Length\:of\:the\:side)$

Perimeter of the square made using the wire = 4 * 21 = 84 cm

We know that,

The perimeter of the regular hexagon = $6 *(Length\:of\:side)$

Let the length of each of the regular hexagon be x

Perimeter of the regular hexagon made using the wire = 6x

As the perimeter of both the figures are same

Therefore,

⇒$84 = 6x$

⇒$x = \frac{84}{6}$

⇒$x = 14$

• Extra-Information

i) Perimeter of triangle = Sum of all the sides

ii) Area of triangle = $\frac{bh}{2}$

iii) Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

where $s = \frac{(a+b+c)}{2}$ and a, b,c are the sides of the triangle