Find the area of the shaded region

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In summary, to find the area of the shaded region, you must first identify the shape of the shaded region and use the appropriate formula to calculate its area. You will also need to know the dimensions of any non-shaded regions present. Using a calculator can be helpful, but it is important to show your work for accuracy. Additionally, for complicated shaded regions, you can break them into smaller shapes and add the areas together to find the total area. It is important to note that different shapes have different formulas for finding their area.
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In the figure, A, B and C are the centres of three equal circles, each of radius 1 cm. Find the area of the shaded region.

I feel stump with this question. Thanks
 

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First, notice that the problem has lots of symmetry, so you might be able to save some work at some point. Now, the distances [itex]\|AB\|, \ \|AC\|, \ \|BC\|[/itex] are all 1cm (see why?). Can you construct any triangles that you can find the areas of? Can you construct any circular arcs that you can find the areas of?
 
  • #3


No problem! Finding the area of the shaded region can be tricky, but we can break it down into smaller steps to make it easier. First, we need to identify the shape of the shaded region. In this case, it is a triangle formed by the centers of the three equal circles. Next, we can find the side lengths of this triangle by drawing lines from each center to the opposite vertex. These lines will form three equilateral triangles with side lengths of 2 cm (1 cm radius + 1 cm radius).

To find the area of the shaded region, we can use the formula for the area of a triangle: 1/2 * base * height. The base of our triangle is 2 cm and the height can be found by drawing a line from the center of one circle to the midpoint of the opposite side, creating a right triangle with a height of 1 cm (half of the base).

So, the area of the shaded region is 1/2 * 2 cm * 1 cm = 1 cm^2. Therefore, the area of the shaded region is 1 cm^2. I hope this helps!
 

1. How do you find the area of the shaded region?

The area of the shaded region can be found by first identifying the shape of the shaded region. Then, use the appropriate formula for the shape to calculate its area. Finally, subtract the area of any non-shaded regions from the total area to find the area of the shaded region.

2. What information do I need to find the area of the shaded region?

You will need to know the shape of the shaded region and the dimensions (length, width, radius, etc.) of any non-shaded regions that may be present. If the dimensions are not given, you may need to use other information provided to calculate them.

3. Can I use the same formula to find the area of any shaded region?

No, the formula for finding the area of a shape varies depending on the shape of the shaded region. For example, the formula for finding the area of a circle is different from the formula for finding the area of a rectangle.

4. Is there a shortcut for finding the area of a complicated shaded region?

Yes, in some cases, you can break the complicated shaded region into smaller, simpler shapes and find the area of each shape separately. Then, add the areas together to find the total area of the shaded region.

5. Can I use a calculator to find the area of the shaded region?

Yes, you can use a calculator to find the area of the shaded region, as long as you have the correct formula and all the necessary dimensions. However, it is always recommended to show your work and calculations to ensure accuracy.

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