Question

Suppose the length of each side of a regular hexagon ABCDEF is 5 cm. Can the length of FB be 8 cm? If not, what is its correct length?
[please solve the Q. 2 (ii)] ​

Answer 1

Answer:

FB is 9.92 cm

Step-by-step explanation:

The triangle ΔFAB is the sum of two right triangles, then  by Pythagoras theorem we can know FB length.

Let P be the point in the middle of FB.

We want to know AP, then we can devide 360/6 = 60, becuas this is a hexagon, then if we divide one of the six triangles in the midle, we get a triangle with a 30º angle and an opposite side of 5/2 = 2.5 cm.

Then applying trigonometry rules we will get sen(30º) = $\frac{2AP}{2.5}$

⇒ 2AP = 2.5 x sen(30º) = 1.25 ⇒ AP = 0.625

Then lets consider the triangle ΔFAP.

Then by Pythagoras theorem:

$5^{2} = 0.625^{2} + FP^{2}$

⇔ FP = $\sqrt{24.61}$ = 4.96 cm

We know that FP = 2FB, then FB = 4.96 x 2 = 9.92 cm

Hence, it can not be 8 cm.

Answer 2

Answer:

The length of FB is not equal to 8 cm

The correct value of FB = 8.66 cm

Step-by-step explanation:

It is given a hexagon ABCDEF

Each angle of hexagon is 120°.

Consider the triangle ABF, the poit of intersection of FB and AD is called as P.

To find BF

Triangle APF, is aright angled triangle,

AF is the hypotenuse. And the angles are in the ratio 30° , 60° and 90°Therefore sides are in the ratio, 1 :√3 : 2

Here AF = 5 cm

AP : PF : AF = 2.5 : 2.5√3 : 5

BF = 2 * PF = 2 * 2.5√3

BF = 8.66