It says:
Find the area of a rectangle with length 12 inscribed in a circle with radius 7.5.
I know when they're talking about a radius with a figure, they're talking about the length between the center of the circle to a corner of the figure. But that usually works only with a regular figure, and a rectangle isn't one.
Does anyone have any ideas on how to solve it?
Since the radius is 7.5, then the diameter is 15. Doesn't that make your rectangle 12 by 15?
108
Oh wait! I see where you're getting at. I think since the diameter of the circle is 15, it will make a diagonal within the rectangle to make a right triangle. Therefore, the dimensions of the rectangle are 12 by 9.
Thanks soooooo much, Ms. Sue! You helped me a lot. (the diameter thing got me going! lol)
You're very welcome. :-)
since the radius is 7.5 the diameter will be 15 units.
from the pythagoras theorem Dsqaure=12Square + XSquare, where x= the unknown quantity.
Therfore; x= Root of((15x15) - (12x12)) = 9
Thank you!
Well, you're right that a rectangle isn't a regular figure, but don't worry, I'm here to help you with a bit of clownish geometry!
To find the area of the rectangle inscribed in a circle, we'll need to rely on some circus tricks, I mean formulas. Here's what we can do:
Step 1: Find the diagonal of the rectangle.
Since the diagonal of the rectangle is also the diameter of the circle, and we know the radius of the circle is 7.5, we can use the Pythagorean theorem to find the length of the diagonal. Let's call it "d."
Using the Pythagorean theorem, we have:
d^2 = (2 * radius)^2 + (2 * length)^2
Step 2: Use the diagonal to find the dimensions of the rectangle.
Now that we know the length of the diagonal, we can use it as the hypotenuse of a right triangle formed by the length and width of the rectangle.
Since the hypotenuse is the diagonal (d), and the length and width are two sides (l, w), we have:
d^2 = l^2 + w^2
Step 3: Find the area of the rectangle.
Finally, now that we have the length (l) and width (w) of the rectangle, we can simply multiply them together to find the area:
Area = length * width
So, using these clownish steps, you should be able to find the area of the rectangle inscribed in the given circle. Good luck with your circus math!
To find the area of a rectangle inscribed in a circle, you can use the fact that the diameter of the circle is equal to the diagonal of the rectangle.
In this case, we can find the diagonal of the rectangle using the Pythagorean theorem. The length of the rectangle is given as 12 inches, and the radius of the circle is given as 7.5 inches.
The diagonal of the rectangle is equal to the diameter of the circle, which is twice the radius. So, the diagonal of the rectangle is 2 * 7.5 = 15 inches.
Now, we can use the Pythagorean theorem to find the width of the rectangle. Let's assume the width of the rectangle is x inches. We have:
x^2 + 12^2 = 15^2
x^2 + 144 = 225
x^2 = 81
x = 9
So, the width of the rectangle is 9 inches.
Now that we have both the length and width of the rectangle, we can calculate the area. The area of a rectangle is given by the formula A = length * width.
Therefore, the area of the rectangle is 12 * 9 = 108 square inches.