Question

**BRAINLIEST IF ANSWERED***

Answer 1

Answer:

(D)7 in.

Step-by-step explanation:

A regular hexagon can be divided into six equilateral triangles.

Therefore:

$b=\dfrac{c}{2}$

Applying Pythagoras Theorem

$c^2=12^2+b^2\\c^2=12^2+(\frac{c}{2})^2\\c^2-(\frac{c}{2})^2=12^2\\c^2-\dfrac{c^2}{4}=144\\\dfrac{4c^2-c^2}{4}=144\\\dfrac{3c^2}{4}=144\\ Cross multiply\\3c^2=144 \times 4\\3c^2=576\\ Divide both sides by 3\\c^2=192\\ Therefore:\\c=\sqrt{192}\\c=8\sqrt{3} in.$

Recall that b=c/2

Therefore:

$b=4\sqrt{3} \approx 7 in.$

The value of b is 7 inches.