<p>this question has a picture, so it would be useful if you owned the book:</p>
<p>pg 738 #20</p>
<p>gracias in advance.</p>
<p>im working on it ill get back to you in a few minutes so hang on</p>
<p>couldnt get it! ack! but i did get one thing: make sure you don't mistakenly assume that the rectangle has dimensions 6 and 2.</p>
<p>the reason I didn't get it was the fact that i didn't know the arc length formula. if you know thatyou can get it. look it up.</p>
<p>thanks for you input.. anyone else????</p>
<p>im not sure if you already looked at this from the consolidated list of blue book problems, but it may help.</p>
<p>My explanation might be a bad one, but it works:
First, you know that the figure is 1/4 of a circle. So you take the 6 (radius), and multiply it by 2 to get the diameter. Therefore, the circumference of the whole circle is 12pi. Then since the arc is 1/4, divide 12pi by 4. You are left with 3pi. 3 pi is the perimeter of the arc.</p>
<pre><code> Now, you know the length + width is 8, and I noticed that there was no note on the bottom saying that the figure was not drawn to scale, so I assumed that it was drawn to scale. I also found that line BC (perpendicular to RT) was in the middle of RT. Therefore, since I knew that RT was 6, I assumed RC was 3. Then I assumed that AR was 5, since it looks right, and 8-3=5. I found the length of the hypotenuse using Pythagorean Theorum, and found that it was approx. 5.83. Then I added 5.83 to 3pi, so I had 5.83+ 3pi so far.
Then I needed to find the length of SA, and knew it would be 1, since AR was 5, and SR was 6. So add 1 to 5.83 + 3pi, and I got 6.83+ 3pi. Then I added CT (3) because RC was 3, and RT was 6. So, I added 3 to 6.83 + 3pi. So I got 9.83 + 3pi, which was closest to answer B) 10 + 3pi. I checked and the answer was B.
</code></pre>
<p>Does anyone else know how to do it better??</p>
<p>Don't allow yourself to get confused! It's all simple if you stay relaxed.</p>
<p>You can easily find the length of arc ST, because you are given the radius and told that it is 1/4 of the circle. So simply use the formula for circumference of a circle with radius 6, then multiply by 1/4 to get arc ST = (1/4) * 12pi = 3pi.</p>
<p>The rest is a simple bit of logic and critical reading. </p>
<p>You know the radii that the shaded area is bound in are all 6. So label SR =6 and RT=6. Now we have 12 + 3pi. </p>
<p>Here's where the critical reading comes in: you had to catch that they told you "the length plus the width of rectangle ABCR is 8."</p>
<p>Well, knowing that, you can do 12 + 3pi - 8 = 4 + 3pi to get the perimeter of the shaded region sans the diagonal AC.</p>
<p>So all you have to find now is the length of diagonal AC. Sounds hard, right? Wrong. Draw a straight line from R to B. It's a radius of the circle, right? We're told the radius is 6. And obviously, the diagonals of a rectangle are equal, so the distance from R to B is the same as the distance from A to C. Add 6 to your current equation (4+3pi) to get 10+3pi, which is answer choice D.</p>
<p>the answer was B. but your answer was correct.</p>
<p>THANKS MUCHISIMO GUYS!</p>
<p>Haha, yeah, after you solve it my way, make sure you have the intelligence to circle the right letter, unlike me.</p>
<p>:-)</p>