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3 years ago

Help me match these formulas pleasee:(

1 answer:

6 0

1. $A= \frac{ah_a}{2},P=a+b+c$
2. $A= \frac{r^2\pi\alpha}{360^o}$
3. $l= \frac{r\pi\alpha}{180^o}$
4. $A=ab,P=2(a+b)$
5. $C=2r\pi$
6. $A=r^2\pi$
7. $P=na,S_n=(n-2)180^o,\alpha= \frac{S_n}{n}$
8. $P=3a,A= \frac{a^2\sqrt{3}}{4}$

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Answer:

If the octagon is clockwise, then after 5 times 45 increments A' will coincide with F.

If the octagon is counterclockwise, then after 3 times 45 increments A' will coincide with F.

Step-by-step explanation:

Case 1: Let the octagon is clockwise

It is given that a regular octagon ABCDEFGH rotates 360 degree clockwise about it's center.

There are 8 vertices and the central angle between two consecutive vertices is 45 degrees.

Central angle between AB is 45 degree.

Central angle between AC is

$\text{Angle between AB}+\text{Angle between BC}=45^{\circ}+45^{\circ}=2\times 45^{\circ}$

Central angle between AD is

$\text{Angle between AB}+\text{Angle between BC}+\text{Angle between CD}=45^{\circ}+45^{\circ}+45^{\circ}=3\times 45^{\circ}$

Similarly,

Central angle between AE is

$4\times 45^{\circ}$

Central angle between FA is

$5\times 45^{\circ}$

Therefore after 5 times 45 increments A' will coincide with F.

Case 2: Let the octagon is counterclockwise

$FA=AH+HG+GF$

$FA=45^{\circ}+45^{\circ}+45^{\circ}$

$FA=135^{\circ}$

$FA=3\times 45^{\circ}$

Therefore after 3 times 45 increments A' will coincide with F.

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Answer:

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Step-by-step explanation:

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