What is the sum of the geometric series i =i

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

adell [148]

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.

4 0

3 years ago

Find the values of X and Y in an isosceles triangle where one angle is 47°

vladimir1956 [14]

Answer:

X and Y = 66.5°.

Step-by-step explanation:

I am assuming that X and Y are the base angles, which are equal in an isosceles triangle.

X = Y = (180 - 47) / 2

= 66.5°.

6 0

3 years ago

Help please important

Lemur [1.5K]

1) tan 41°= 30cm divide by y cm
y= 30 divide by tan-1 41°

3 0

3 years ago

Read 2 more answers

"Sam" and "Martha" are the local names for two lighthouses that guard a particularly dangerous part of the coast. Sam blinks eve

Hunter-Best [27]

Answer:

Sam and Martha will blink again in 24 seconds :)

4 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP IM STUCK HELP PLEASE

sasho [114]

Answer:

x>-2 and x<5

-2 <x<5

Step-by-step explanation:

We have open circles at -2 and 5 and are between the two numbers so we have and AND statement. It can be written either

x>-2 and x<5

or

-2 <x<5

6 0

3 years ago