Area of shaded region
- Thread starter zipy147
- Start date
Step-by-step teaching can't be done here...not a classroom.
Start by learning about circle segments:
http://www.google.ca/search?hl=en&sourc ... =&gs_rfai=
Start by learning about circle segments:
http://www.google.ca/search?hl=en&sourc ... =&gs_rfai=
Here are some tips:
Whenever you have geometric figures like this, add some useful lines of your own.
In this case, draw four radii, one to each corner of the shaded area.
Those radii combined with the segment labeled "2" will create a bunch of 60 degree angles at the center of the circle.
It also creates several 30-60-90 triangles.
This reveals to us that the radius of the circle is 2.
Next, if you calculate areas of 120 degree sectors and subtract the appropriate triangle areas, you will have the area of the white sections.
Subtract the two white sections from the total area of the triangle, and that is the shaded area.
If you need review on finding areas, try:
http://mathworld.wolfram.com/CircularSegment.html
Whenever you have geometric figures like this, add some useful lines of your own.
In this case, draw four radii, one to each corner of the shaded area.
Those radii combined with the segment labeled "2" will create a bunch of 60 degree angles at the center of the circle.
It also creates several 30-60-90 triangles.
This reveals to us that the radius of the circle is 2.
Next, if you calculate areas of 120 degree sectors and subtract the appropriate triangle areas, you will have the area of the white sections.
Subtract the two white sections from the total area of the triangle, and that is the shaded area.
If you need review on finding areas, try:
http://mathworld.wolfram.com/CircularSegment.html
Although the sketch supplied is "not to scale", the center of the circle can be found by symmetry considerations. The arcs are 120, 60, 120, 60. Therefore the shaded region must be positioned such that lines drawn from its four corners (diagonals) will pass through the center of the circle.