Find Area of Triangle QLP & XYZ in Hexagon

In summary, the conversation discusses finding the area of a hexagon formed by attaching 3 squares to each side of a right angled triangle. It also mentions finding the area of two triangles within the figure. The solution involves using the formula for the area of a triangle and repositioning some shapes to form a rectangle.
  • #1
ritwik06
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0

Homework Statement



A right angled triangle has 3 squares attached to each side(the measure of each is givn in the figure). a hexagon is thus formed. Find its area.

Homework Equations



none

The Attempt at a Solution


I have found the area of the figure except for the following triangles.
triangle QLP and triangle XYZ
Please help me with these two triangles!
 
Last edited:
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  • #2
The figure is here

The figure is here
 

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  • #3
It may help to know that you can find the area of a triangle to be:

[tex]A = \frac{1}{2}ab\sin C[/tex]
 
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  • #4
You want the sum of the areas of four regions:

Two are squares, and two are triangles which together can be repositioned to form a rectangle. a*a, b*b, and two of a*b.
 
  • #5
Thanks, the problem seems solved. Thanks a lot!
 

1. How do you find the area of a triangle in a hexagon?

To find the area of a triangle in a hexagon, you can use the formula A = (1/2)bh, where A is the area, b is the base of the triangle, and h is the height of the triangle. In a hexagon, the base and height of the triangle will be the same as the side length of the hexagon.

2. Can you use any formula to find the area of a triangle in a hexagon?

Yes, you can also use Heron's formula, which is A = √(s(s-a)(s-b)(s-c)), where A is the area, s is the semi-perimeter of the triangle, and a, b, and c are the lengths of the triangle's three sides. Just make sure to divide the hexagon into two triangles and use the correct side lengths in the formula.

3. What if the triangle is not a right triangle?

If the triangle is not a right triangle, you can still use the same formulas mentioned above. Just make sure to use the correct side lengths and height of the triangle in the formula. You may also need to use trigonometric functions to calculate the height of the triangle.

4. Is it possible for a hexagon to have more than one triangle within it?

Yes, it is possible for a hexagon to have more than one triangle within it. In fact, a regular hexagon has six equal triangles within it. You can use the same formulas mentioned above to find the area of each triangle within the hexagon.

5. Are there any other methods to find the area of a triangle in a hexagon?

Yes, there are other methods such as using the Pythagorean theorem or the Law of Cosines. However, these methods may be more complex and require additional calculations. It is generally easier to use the formulas mentioned above to find the area of a triangle in a hexagon.

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