Thread: Trapezoid within a Circle Area Question

1. Re: Trapezoid within a Circle Area Question

Is there a question?

2. Re: Trapezoid within a Circle Area Question

We do not do homework.

3. Re: Trapezoid within a Circle Area Question

I've learned that as a newb on the forum not to edit a post more than once, or it vanishes!

4. Re: Trapezoid within a Circle Area Question

What post.
We haven't seen a problem from you.
Please post the problem you want help with...you hockey puck

5. Re: Trapezoid within a Circle Area Question

LOL Dan told me to wait, and it should reappear. Nice to see some eager helpers here! Okay here we go... gonna try one more time

You got this circle:

https://i.imgsafe.org/e92d938fb2.jpg

The lines from A to B and C to D are parallel.

How can you show that the area of the trapezoid ABCD can be expressed as:

Area = 1/2 R^2 sin theta - 1/2r^2 sin 2theta

6. Re: Trapezoid within a Circle Area Question

see attached diagram ...

Area triangle adb = $\dfrac{1}{2}r^2 \sin(2\theta-180) = \dfrac{1}{2}r^2\bigg[\sin(2\theta)\cos(180)-\cos(2\theta)\sin(180)\bigg] = \dfrac{1}{2}r^2\bigg[-\sin(2\theta)\bigg] = -\dfrac{1}{2}r^2 \sin(2\theta)$

Area triangle bdc = $\dfrac{1}{2}r^2 \sin(180-\theta) = \dfrac{1}{2}r^2\bigg[\sin(180)\cos{\theta}-\cos(180)\sin{\theta}\bigg] = \dfrac{1}{2}r^2\sin{\theta}$

sum of the areas = $\dfrac{1}{2}r^2\sin{\theta} - \dfrac{1}{2}r^2 \sin(2\theta)$

7. Re: Trapezoid within a Circle Area Question

LOL Dan told me to wait, and it should reappear. Nice to see some eager helpers here! Okay here we go... gonna try one more time You got this circle:
https://i.imgsafe.org/e92d938fb2.jpg
Area = 1/2 R^2 sin theta - 1/2r^2 sin 2theta
I replied to your post but it too disappeared.
I gave two valuable webpages: circular segments & circular sectors.

Use Skeeter's diagram and the pages are try to work it out for your self.

8. Re: Trapezoid within a Circle Area Question

Thanks everyone for your timely help! And to imagine I did a math minor in university. My profs are rolling in their graves I bet! I used to be pretty good at math back in high school and university. I even took intermediate calculus back in the day, but well that was like 3 decades ago so I've forgotten a few things... sigh... I think I even posted in the wrong section... maybe this is more Geometry? Anyways, have a nice weekend!