bandOFhorses:
a) Each vertex angle of the regular n-gon measures (n-2)*180/n degrees. Since each isosceles triangle uses one vertex angle, the measure of the vertex angle of each isosceles triangle is (n-2)*180/n degrees.

b) The base angles of each isosceles triangle are congruent. Since the vertex angle measures (n-2)*180/n degrees, and the three angles of a triangle sum to 180 degrees, each base angle measures (180 - (n-2)*180/n)/2 = (180/n) degrees.

c) Let's draw a diagram. If s is the length of each side of the regular n-gon, then the base of each isosceles triangle is s. Using trigonometry, the altitude h to the base bisects the vertex angle, so:

h/s = sin((n-2)*180/2n)
h = s*sin((n-2)*180/2n)

d) The area of each isosceles triangle is (1/2)*b*h = (1/2)*s*[s*sin((n-2)*180/2n)] = (1/2)*s^2*sin((n-2)*180/2n).

e) There are n isosceles triangles that make up the regular n-gon. So the total area is:
A = n*(1/2)*s^2*sin((n-2)*180/2n)
= (1/2)*n*s^2*sin((n-2)*180/2n)

bandOFhorses:
a) Each vertex angle of the regular n-gon measures (n-2)*180/n degrees. Since each isosceles triangle uses one vertex angle, the measure of the vertex angle of each isosceles triangle is (n-2)*180/n degrees.

b) The base angles of each isosceles triangle are congruent. Since the vertex angle measures (n-2)*180/n degrees, and the three angles of a triangle sum to 180 degrees, each base angle measures (180 - (n-2)*180/n)/2 = (180/n) degrees.

c) Let's draw a diagram. If s is the length of each side of the regular n-gon, then the base of each isosceles triangle is s. Using trigonometry, the altitude h to the base bisects the vertex angle, so:

h/s = sin((n-2)*180/2n)
h = s*sin((n-2)*180/2n)

d) The area of each isosceles triangle is (1/2)*b*h = (1/2)*s*[s*sin((n-2)*180/2n)] = (1/2)*s^2*sin((n-2)*180/2n).

e) There are n isosceles triangles that make up the regular n-gon. So the total area is:
A = n*(1/2)*s^2*sin((n-2)*180/2n)
= (1/2)*n*s^2*sin((n-2)*180/2n)

Shellsploit:
chatGP left the group chat

CHRISTFUCKER:
Do your homework by yourself

turmacs:
idiot

turmacs:
I know this answer but i don't know how do the workings to get the answer. So far, none of my workings have been able to lead me to the correct answer.
Please can any one show me the workings?

turmacs:
I know this answer but i don't know how do the workings to get the answer. So far, none of my workings have been able to lead me to the correct answer.
Please can any one show me the workings?

Wizyoung:


Were you getting answers like:

(a) A vertex angle = 540 -180n

(b) One base angle of one triangle = (n - 2) × 90

You might want to check your source answer to be sure that the screenshot answers are the corresponding answers to the questions asked.

I can solve all for you but had to stop at a. and b. given the difference in answers.

The Answers above are absolutely correct.

turmacs:
baba, with all due respect, sorry to say but you dey solve rubbish

Wizyoung:


No vex...

I forgot to divide the sum of interior angle by n.

If you do the division, you'd arrive at the correct answer as shown from my solution above.

You need to be polite towards people attending to your queries though.

turmacs:
These are the correct answers but the thing is that I'm having problems arriving at the answers.

turmacs:
I know this answer but i don't know how do the workings to get the answer. So far, none of my workings have been able to lead me to the correct answer.
Please can any one show me the workings?

turmacs:
I know this answer but i don't know how do the workings to get the answer. So far, none of my workings have been able to lead me to the correct answer.
Please can any one show me the workings?

turmacs:
I know this answer but i don't know how do the workings to get the answer. So far, none of my workings have been able to lead me to the correct answer.
Please can any one show me the workings?