Geometry Problem: Find Overlapping Area

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In summary, the problem involves finding the area of the region where two congruent triangles overlap after being cut from a larger rectangle. The solution involves creating four smaller triangles and proving that they all have the same area, resulting in the overlap area being 2/3 the area of one of the original triangles.
  • #1
preet
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I can't get this problem... no idea how to do it. Can't use coordinates / angles, just straightforward geometry. (by angles I mean, you can't use a calculator to find em, then do everything from there)

Any help appreciated... thanks

"A card 12cm long and 6 cm wide is cut along a diagonal to form two congruent triangles. The triangles are arranged as shown. Find the area of the region where the triangles overlap."

http://img314.imageshack.us/img314/7241/untitled8ew.gif
 
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  • #2
Draw a line segment from the right angle to the intersection of the two hypotenuses. You now have four small triangles. It should be evident (i.e. you should be able to prove) that all four triangles have the same area. It follows that the area of the overlap region is 2/3 the area of one of the original triangles.
 
  • #3
Nice solution!
 

1. What is the purpose of finding the overlapping area in a geometry problem?

The purpose of finding the overlapping area in a geometry problem is to determine the shared space between two or more shapes. This can be useful in various real-life scenarios, such as calculating the amount of land that overlaps between two properties or determining how much paint is needed to cover an area with multiple overlapping shapes.

2. How do you find the overlapping area in a geometry problem?

To find the overlapping area, you first need to identify the shapes that are overlapping. Then, you can use various formulas and techniques, such as the area of intersection formula, to calculate the shared space between the shapes. It is important to use the correct formula and accurately measure the dimensions of the shapes for an accurate result.

3. Can a geometry problem have more than two overlapping shapes?

Yes, a geometry problem can have more than two overlapping shapes. In fact, the more shapes that are involved, the more complex the problem becomes. It is important to carefully identify and measure each shape and use the appropriate formulas to calculate the overlapping area.

4. What are some real-life applications of finding the overlapping area in geometry?

Finding the overlapping area in geometry has many practical applications. For example, it can be used in engineering to calculate the shared space between different building structures. It is also useful in art and design, such as determining the overlap between different layers in a painting or graphic design. Additionally, it is commonly used in landscaping and architecture to determine the overlap between different land features or building designs.

5. Are there any shortcuts or tricks for finding the overlapping area in a geometry problem?

While there are no specific shortcuts or tricks, there are some strategies that can make finding the overlapping area easier. For example, breaking the shapes into smaller, simpler parts and then calculating the overlapping area for each part can help to visualize and solve the problem. Additionally, using graph paper or a computer program can make it easier to accurately measure and calculate the overlapping area.

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