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Rhombus ABCD has perimeter 148, and one of its diagonals has length 28. what is the area of ABCD?

 Jun 26, 2021
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Rhombus ABCD has perimeter 148, and one of its diagonals has length 28. what is the area of ABCD?    

 

First, draw it.  Draw a rhombus, then draw its shorter diagonal. 

 

All sides of a rhombus are equal, so each side is 148/4 = 37.  Think of it as a square tilted like an old, falling-over shed. 

 

One of the diagonals is 28, but which one?  IF the figure were a square, its diagonal would be 37 • sqrt(2) = 52.3. 

 

When you tilt the square over to form the rhombus, one diagonal gets longer and the other diagonal gets shorter. 

 

Therefore, the shorter diagonal is 28. When you draw it, you'll see an isoceles triangle whose sides are 37, 37, and 28.  

 

Can you use this information to calculate the height of the rhombus?  Area = base • height.  Can you take it from there?  

 Jun 26, 2021

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