Pretty much there is a square with a height and width of $2$", inside there is a perfect circle with radius $1$". Also overlapping the circle and square is a isosceles triangle also with height $2$" and width of the bottom to be $2$". (Truly to see what I'm talking about, you have to click on the image). What is the area of the shaded (gray) region inside of the square not overlapped by the circle or the triangle?
[Math] How to find area of remaining square with shapes inside
area
Related Solutions
The area of the parellelagramm is base times height. You know figured out the height. So the base is the radius of the circle. You know that.
What is the area of the circle wedge? Well the entire circle is 360 degrees so this is just 30 degrees. It's a specific proportion of the entire circle. So if you can find the area of the entire circle you can find the area of the circle wedge.
The area of the shaded area is the area of the paralelagram minus the area of the circle wedge.
The circle of radius R in the square of side C is such :
$ 2 R = C$
Area of the circle $\pi R^2$ , of the square $C^2$ , and the ratio of circle on square is :
and the ratio is : $\pi \frac{R^2}{C^2} = \pi \frac{R^2}{4 R^2} = \frac{\pi}{4} $
If the area of the square is $100 cm^2$ , the circle will have an area of $\frac{\pi}{4} 100 cm^2 \approx 78.54 cm^2$
The square of side C in the circle of radius R is such :
$C^2 = R^2 + R^2$
similarly the ratio is : $\pi \frac{R^2}{C^2} = \pi \frac{R^2}{2 R^2} = \frac{\pi}{2} $
If the area of the square is $100 cm^2$ , the circle will have an area of $\frac{\pi}{2} 100 cm^2 \approx 157,08 cm^2$
Best Answer
Hint: You know the area of the square and the area of the circle, so the question is the area of the funny shapes in the lower left and right corners. In problems like these, you should look for ways to cut up the shapes into something you know. I added two lines and got this
Now your funny shapes are triangles less the bulge of a circle around the secant. That bulge is the difference between a sector of a circle and a triangle. You need to find the coordinates of the intersection of the circle and the downward lines from the top center of the square. Then find the angle the secant from there to the bottom center represents.