Find Area of Rhombhus In Triangle ABC

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In summary, the conversation discusses finding points X, Y, and Z on the sides of triangle ABC to form a rhombus AXYZ. The area of this rhombus is shown to be less than or equal to half the area of triangle ABC. The conversation also mentions the use of angle and perpendicular bisectors, but the individual has not been able to proceed further.
  • #1
vaishakh
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In triangle ABC, find points X, Y and Z on AB, BC and CA such that AXYZ is a rhombhus. Show that area of the rhombhus AXYZ<= 1/2A(ABC)
 
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  • #2
You have posted a number of questions without any indication what, if anything, you have done on it yourself. We will not do your homework for you! We will try to give hints but we need to know what you have tried so we can gauge your understanding and see where you are going wrong.
 
  • #3
i tried with the trapezium BXZY and CYXZ. but couldn't reah nowhere. after that a close look made me understand thatAY is the angle bisectors and XZ is its pependicular bisector. but i don't know how to use this property to move on. but i wrote all ratios i willget like- AB/AC = BY/CY. but the need is AX + AZ + 1/2(AB + AC)
 

FAQ: Find Area of Rhombhus In Triangle ABC

What is the formula for finding the area of a rhombus in triangle ABC?

The formula for finding the area of a rhombus in triangle ABC is (base x height)/2. This is because a rhombus is a parallelogram with all sides equal, and the area of a parallelogram is base x height.

How do you find the base and height of a rhombus in triangle ABC?

To find the base and height of a rhombus in triangle ABC, you can use the Pythagorean theorem. The base of the rhombus will be one of the sides of the triangle, and the height can be found by drawing a perpendicular line from the base to the opposite vertex of the rhombus.

Can you find the area of a rhombus in triangle ABC without knowing the height?

Yes, you can find the area of a rhombus in triangle ABC without knowing the height. If you know the length of the base and the measure of one angle of the rhombus, you can use the sine function to find the height. Then, you can plug the values into the formula (base x height)/2 to find the area.

How is the area of a rhombus in triangle ABC related to the area of the triangle itself?

The area of a rhombus in triangle ABC is half the area of the triangle. This is because the rhombus divides the triangle into two equal parts, and the area of a rhombus is half the product of its diagonals.

Can you use the same formula to find the area of a rhombus in any triangle?

Yes, the formula (base x height)/2 can be used to find the area of a rhombus in any triangle. As long as the rhombus is formed by drawing a diagonal from one vertex to the opposite side of the triangle, the formula will work.

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