Question

Compare the perimeters of the two regular figures. Which statement is true?

Answer 1

Answer:

(A). The perimeter of the octagon is greater than that of the hexagon.

Step-by-step explanation:

Since, hexagon consists of 6 sides and 6 angles, thus the measure of one angle of the hexagon will be=$\frac{(n-2){\timeS}180^{\circ}}{6}$

=$\frac{(6-2){\timeS}180^{\circ}}{6}$

=$\frac{(4){\timeS}180^{\circ}}{6}$

=$120^{\circ}$

Now, since MQ is the angle bisector of the one of the angle of the hexagon, therefore ∠QMP=60°.

Now, from ΔQMP. we have

$\frac{MP}{MQ}=cos60^{\circ}$

$MP=\frac{1}{2}$

Thus, the perimeter of the hexagon is:

$P=12{\times}MP$

$P=12{\times}\frac{1}{2}$

$P=6 units$

Thus, the perimeter of hexagon is 6 units.

Also, Since, octagon consists of 8 sides and 8 angles, thus the measure of one angle of the octagon will be=$\frac{(n-2){\timeS}180^{\circ}}{8}$

=$\frac{(8-2){\timeS}180^{\circ}}{8}$

=$\frac{(6){\timeS}180^{\circ}}{8}$

=$135^{\circ}$

Now, since AP is the angle bisector of the one of the angle of the octagon, therefore ${\angle}PAC=cos\frac{135}{2}$.

From ΔAPC, we have

$AC=cos\frac{135}{2}$

Now, Perimeter of octagon is:

$P=16{\times}cos\frac{135}{2}$

$P=16{\times}0.382$

$P=6.122 units$

Thus, the perimeter of octagon is 6.122 units.

Now, the perimeter of octagon is greater than perimeter of the hexagon, thus option A is correct that is The perimeter of the octagon is greater than that of the hexagon.